COORDINATE TRANSFORMATION FROM EDDINGTON-FINKELSTEIN TO FEFFERMAN-GRAHAM COORDINATES FOR GRAVITY DUAL TO BOOST-INVARIANT FLOW

SUPPLEMENTARY MATHEMATICA NOTEBOOK TO VER. 2 OF 0805.3774 [hep-th]

AUTHOR: MICHAL.HELLER@UJ.EDU.PL

07.11.2008

OVERVIEW :
 
 In order to find a coordinate transformation from EF to FG variable up to the third order in the gradient expansion, one needs to solve Einstein eqns explicitely in the third order. This is done in sections

EF PART
and
FG PART

The transformation is described in all details in the section

COORDINATE TRANSFORMATION

EF PART

Einstein EQNS in EF coordinates

Quit[];

coord = {r,t,y,x1,x2};

metricsign=-1;

$Assumptions= And[t∈Reals,x1∈Reals,x2∈Reals,r∈Reals,th1∈Reals,th2∈Reals,th3∈Reals,th4∈Reals,th5∈Reals,r>0,w>0];

metric=(({{0, 1, 0, 0, 0}, {1, -(r^2)AEF[t,r], 0, 0, 0}, {0, 0, (((r t+1))^2)Exp[bEF[t,r]], 0, 0}, {0, 0, 0, (r^2)Exp[cEF[t,r]], 0}, {0, 0, 0, 0, (r^2)Exp[cEF[t,r]]}}));

<<diffgeo.m

einsteinEqns=Union[Flatten[RicciTensor+4 metric]];

eqn1=Expand[einsteinEqns[[2]]];
eqn2=Expand[einsteinEqns[[3]]];
eqn3=Expand[einsteinEqns[[4]]];
eqn4=Expand[einsteinEqns[[5]]];
eqn5=Expand[einsteinEqns[[6]]];

AEF[t_,r_]:=AEF0[r ((t
)^(1/3))]+(1/(t^(2/3)))AEF1[r (t^(1/3))]+(1/(t^(4/3)))AEF2[r (t^(1/3))]+(1/(t^2))AEF3[r (t^(1/3))]+(1/(t^(8/3)))AEF4[r (t^(1/3))];
bEF[t_,r_]:=(1/(t^(2/3)))bEF1[r (t^(1/3))]+(1/(t^(4/3)))bEF2[r (t^(1/3))]+(1/(t^2))bEF3[r (t^(1/3))]+(1/(t^(8/3)))bEF4[r (t^(1/3))];
cEF[t_,r_]:=(1/(t^(2/3)))cEF1[r (t^(1/3))]+(1/(t^(4/3)))cEF2[r (t^(1/3))]+(1/(t^2))cEF3[r (t^(1/3))]+(1/(t^(8/3)))cEF4[r (t^(1/3))];

Here Einstein equations and Riemann squared are expanded up to the third order in 1/(t^(2/3)):

eqn1S=Series[Expand[(t^(-2/3))eqn1//.{r->v (t^(-1/3)),t->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,4}];
eqn2S=Series[Expand[(t^(-4/3))eqn2//.{r->v (t^(-1/3)),t->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,4}];
eqn3S=Series[Expand[(t^(2/3))eqn3//.{r->v (t^(-1/3)),t->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,4}];
eqn4S=Series[Expand[eqn4//.{r->v (t^(-1/3)),t->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,4}];
eqn5S=Series[Expand[(t^(2/3))eqn5//.{r->v (t^(-1/3)),t->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,4}];

eqn1o0=SeriesCoefficient[eqn1S,0];
eqn1o1=SeriesCoefficient[eqn1S,1];
eqn1o2=SeriesCoefficient[eqn1S,2];
eqn1o3=SeriesCoefficient[eqn1S,3];
eqn1o4=SeriesCoefficient[eqn1S,4];

eqn2o0=SeriesCoefficient[eqn2S,0];
eqn2o1=SeriesCoefficient[eqn2S,1];
eqn2o2=SeriesCoefficient[eqn2S,2];
eqn2o3=SeriesCoefficient[eqn2S,3];
eqn2o4=SeriesCoefficient[eqn2S,4];

eqn3o0=SeriesCoefficient[eqn3S,0];
eqn3o1=SeriesCoefficient[eqn3S,1];
eqn3o2=SeriesCoefficient[eqn3S,2];
eqn3o3=SeriesCoefficient[eqn3S,3];
eqn3o4=SeriesCoefficient[eqn3S,4];

eqn4o0=SeriesCoefficient[eqn4S,0];
eqn4o1=SeriesCoefficient[eqn4S,1];
eqn4o2=SeriesCoefficient[eqn4S,2];
eqn4o3=SeriesCoefficient[eqn4S,3];
eqn4o4=SeriesCoefficient[eqn4S,4];

eqn5o0=SeriesCoefficient[eqn5S,0];
eqn5o1=SeriesCoefficient[eqn5S,1];
eqn5o2=SeriesCoefficient[eqn5S,2];
eqn5o3=SeriesCoefficient[eqn5S,3];
eqn5o4=SeriesCoefficient[eqn5S,4];

Procedure xxx[ch] simplifies logarithms of integer numbers

xxx[ch_Integer]:=FactorInteger[ch]/.{List[ah_Integer,bh_Integer]->bh Log[ah],List->Plus}

Orders 0, 1, 2

subsSOL

subsSOLo012={AEF0[v_]->1-(1/((v^4) (w^4))),AEF1[v_]->((2 (1+v w))/(3 (v^5) (w^4)))+((2 D1a (1+(v^4) (w^4)))/(3 (v^5) (w^4))),bEF1[v_]->-(4/(3 v))+((2 D1a)/(3 v))+((π w)/3)-(2/3) w ArcTan[v w]-(4/3) w Log[v]-(4/3) w Log[w]+(2/3) w Log[1+v w]+(1/3) w Log[1+(v^2) (w^2)],cEF1[v_]->(2/(3 v))+((2 D1a)/(3 v))-((π w)/6)+(1/3) w ArcTan[v w]+(2/3) w Log[v]+(2/3) w Log[w]-(1/3) w Log[1+v w]-(1/6) w Log[1+(v^2) (w^2)],AEF2[v_]->(((D1a^2) (-3+(v^4) (w^4)))/(9 (v^6) (w^4)))+((2 D1a (-3-2 v w+3 (v^4) (w^4)))/(9 (v^6) (w^4)))-((2 (D2a+D2a (v^4) (w^4)))/(3 (v^5) (w^4)))+((-2+v w (-4-v w+2 (v^3) (w^3)))/(6 (v^6) (w^4)))+(((1+(v^4) (w^4)) ArcTan[v w])/(3 (v^5) (w^3)))-((Log[2])/(9 (v^4) (w^2)))-((2 Log[v])/(3 (v^4) (w^2)))-((2 Log[w])/(3 (v^4) (w^2)))+((Log[1+(v^2) (w^2)])/(3 (v^4) (w^2))),bEF2'[v_]->bEF2v[v],bEF2v[v_]->((2 (D1a^2))/(9 (v^3)))+((2 D2a)/(3 (v^2)))+((2 π (w^2) (1+v w (1+v w)))/(9 v (1+v w) (1+(v^2) (w^2))))+((4 D1a (1+v w (3+v w (5+v w (7+3 v w (3+v w (2+v w)))))))/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((16+v w (26+v w (43+v w (60+v w (34+11 v w (2+v w))))))/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((w (3+4 v w-7 (v^4) (w^4)) ArcTan[v w])/(9 ((v^2)-(v^6) (w^4))))+(((w^2) Log[16])/(9 v-9 (v^5) (w^4)))+((8 (v^2) (w^5) Log[v])/(9-9 (v^4) (w^4)))+((8 (v^2) (w^5) Log[w])/(9-9 (v^4) (w^4)))+((4 (w^2) (1+v w (1+v w)) Log[1+v w])/(9 v (1+v w) (1+(v^2) (w^2))))+((2 (w^2) (1+v w (-1+v w)) Log[1+(v^2) (w^2)])/(9 v (-1+v w) (1+(v^2) (w^2)))),dEF2[v_]->-(D1a/(3 (v^2)))-((D1a^2)/(6 (v^2)))-(D2a/v)+((π (w^2))/12)-((-4+4 v w)/(12 (v^2)))-((w (-3+v w) ArcTan[v w])/(6 v))-(2/3) (w^2) Log[v]-(2/3) (w^2) Log[w]+(1/6) (w^2) Log[1+v w]+(1/4) (w^2) Log[1+(v^2) (w^2)],cEF2[v_]->-((bEF2[v])/2)+dEF2[v]};

subsSOLo012DER1={AEF0'[v_]->(4/((v^5) (w^4))),AEF1'[v_]->-((2 (5+4 v w))/(3 (v^6) (w^4)))-((2 D1a (5+(v^4) (w^4)))/(3 (v^6) (w^4))),bEF1'[v_]->-((2 D1a)/(3 (v^2)))+(4/(3 (v^2) (1+v w) (1+(v^2) (w^2)))),cEF1'[v_]->-((2 D1a)/(3 (v^2)))-(2/(3 (v^2) (1+v w) (1+(v^2) (w^2)))),AEF2'[v_]->((6+10 v w+(v^2) (w^2)-(v^4) (w^4))/(3 (v^7) (w^4)))-((2 (D1a^2) (-9+(v^4) (w^4)))/(9 (v^7) (w^4)))+((2 D2a (5+(v^4) (w^4)))/(3 (v^6) (w^4)))-((4 D1a (-9-5 v w+3 (v^4) (w^4)))/(9 (v^7) (w^4)))-(((5+(v^4) (w^4)) ArcTan[v w])/(3 (v^6) (w^3)))+((4 Log[2])/(9 (v^5) (w^2)))+((8 Log[v])/(3 (v^5) (w^2)))+((8 Log[w])/(3 (v^5) (w^2)))-((4 Log[1+(v^2) (w^2)])/(3 (v^5) (w^2))),bEF2''[v_]->bEF2v'[v],bEF2v'[v_]->-((2 (D1a^2))/(3 (v^4)))-((4 D2a)/(3 (v^3)))-((2 π (w^2) (1+v w (2+v w (3+2 v w (3+v w (2+v w))))))/(9 (v^2) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((4 D1a (3+v w (11+3 v w (1+v w) (8+v w (6+v w (12+v w (8+3 v w (4+v w (2+v w)))))))))/(9 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((2 (-24+v w (-42+v w (-62+v w (-82+v w (-33+v w (-8+v w (47+v w (102+v w (37+11 v w (2+v w)))))))))))/(9 (v^4) (-1+v w) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((2 w (3+v w (8+v w (13+v w (18+7 v w (3+v w (2+v w)))))) ArcTan[v w])/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((4 (w^2) (-1+5 (v^4) (w^4)) Log[2])/(9 (v^2) (((-1+(v^4) (w^4)))^2)))+((16 v (w^5) (1+(v^4) (w^4)) Log[v])/(9 (((-1+(v^4) (w^4)))^2)))+((16 v ((w^5)+(v^4) (w^9)) Log[w])/(9 (((-1+(v^4) (w^4)))^2)))-((4 (w^2) (1+v w (2+v w (3+2 v w (3+v w (2+v w))))) Log[1+v w])/(9 (v^2) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((2 (w^2) (1+v w (-2+v w (3-2 v w (3+v w (-2+v w))))) Log[1+(v^2) (w^2)])/(9 (v^2) (((-1+v w))^2) (((1+(v^2) (w^2)))^2))),dEF2'[v_]->((2 D1a)/(3 (v^3)))+((D1a^2)/(3 (v^3)))+(D2a/(v^2))-((4+v w (2+3 v w (1+v w)))/(6 (v^3) (1+v w) (1+(v^2) (w^2))))-((w ArcTan[v w])/(2 (v^2))),cEF2'[v_]->-(1/2) bEF2'[v]+dEF2'[v]};

subsSOLo012DER2={AEF0''[v_]->-(20/((v^6) (w^4))),AEF1''[v_]->((4 D1a ((v^4)+(15/(w^4))))/(3 (v^7)))+((20 (3+2 v w))/(3 (v^7) (w^4))),bEF1''[v_]->((4 D1a)/(3 (v^3)))-((4 (2+v w (3+v w (4+5 v w))))/(3 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2))),cEF1''[v_]->((4 D1a)/(3 (v^3)))+((4+2 v w (3+v w (4+5 v w)))/(3 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2))),AEF2''[v_]->((2 (D1a^2) (-21+(v^4) (w^4)))/(3 (v^8) (w^4)))-((4 D2a (15+(v^4) (w^4)))/(3 (v^7) (w^4)))+((4 D1a (-21-10 v w+3 (v^4) (w^4)))/(3 (v^8) (w^4)))+((-42+2 v w (-30+v w (-22+v w (-30-v w+(v^3) (w^3)))))/(3 (v^8) (w^4) (1+(v^2) (w^2))))+((2 (15+(v^4) (w^4)) ArcTan[v w])/(3 (v^7) (w^3)))-((20 Log[2])/(9 (v^6) (w^2)))-((40 Log[v])/(3 (v^6) (w^2)))-((40 Log[w])/(3 (v^6) (w^2)))+((20 Log[1+(v^2) (w^2)])/(3 (v^6) (w^2))),Derivative[3][bEF2][v_]->bEF2v''[v],bEF2v''[v_]->((8 (D1a^2))/(3 (v^5)))+((4 D2a)/(v^4))+((4 π (w^2) (1+3 v w (1+v w (2+v w (1+v w) (3+v w (1+v w (4+v w (2+v w))))))))/(9 (v^3) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((8 D1a (2+v w (9+v w (24+v w (50+v w (82+v w (110+v w (124+v w (114+v w (102+v w (85+6 v w (10+v w (4+v w)))))))))))))/(3 (v^5) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-((2 (96+v w (174+v w (253+v w (332+v w (26+v w (-218+v w (-421+v w (-624+v w (-456+v w (-326+v w (119+3 v w (188+v w (42+11 v w (2+v w)))))))))))))))/(9 (v^5) (((-1+v w))^2) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-((2 w (9+v w (31+3 v w (22+v w (38+v w (48+v w (52+v w (50+7 v w (6+v w (3+v w))))))))) ArcTan[v w])/(9 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((8 (w^2) (1+15 (v^8) (w^8)) Log[2])/(9 (v^3) (((-1+(v^4) (w^4)))^3)))-((16 (w^5) (1+12 (v^4) (w^4)+3 (v^8) (w^8)) Log[v])/(9 (((-1+(v^4) (w^4)))^3)))-((16 (w^5) (1+12 (v^4) (w^4)+3 (v^8) (w^8)) Log[w])/(9 (((-1+(v^4) (w^4)))^3)))+((8 (w^2) (1+3 v w (1+v w (2+v w (1+v w) (3+v w (1+v w (4+v w (2+v w))))))) Log[1+v w])/(9 (v^3) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 (w^2) (1+3 v w (-1+v w (2+v w (-1+v w) (3+v w (-1+v w (4+v w (-2+v w))))))) Log[1+(v^2) (w^2)])/(9 (v^3) (((-1+v w))^3) (((1+(v^2) (w^2)))^3))),dEF2''[v_]->-((2 D1a)/(v^4))-((D1a^2)/(v^4))-((2 D2a)/(v^3))+((6+v w (10+v w (13+v w (2+v w) (8+3 (v^2) (w^2)))))/(3 (v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((w ArcTan[v w])/(v^3)),cEF2''[v_]->-(1/2) bEF2''[v]+dEF2''[v]};

subsSOLo012DER3={Derivative[3][AEF0][v_]->(120/((v^7) (w^4))),Derivative[3][AEF1][v_]->-((20 (7+4 v w))/((v^8) (w^4)))-((4 D1a (35+(v^4) (w^4)))/((v^8) (w^4))),Derivative[3][bEF1][v_]->-((4 D1a)/(v^4))+((8 (3+v w (8+3 v w (5+v w (8+v w (9+v w (8+5 v w)))))))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3))),Derivative[3][cEF1][v_]->-((4 D1a)/(v^4))-((4 (3+8 v w+15 (v^2) (w^2)+24 (v^3) (w^3)+27 (v^4) (w^4)+24 (v^5) (w^5)+15 (v^6) (w^6)))/(3 (v^4) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^3))),Derivative[3][AEF2][v_]->((4 D2a ((v^4)+(35/(w^4))))/(v^8))+((2 (D1a^2) (-4 (v^4)+(168/(w^4))))/(3 (v^9)))+((8 D1a (84+35 v w-6 (v^4) (w^4)))/(3 (v^9) (w^4)))+((336+2 v w (210+v w (337+v w (420+v w (175+v w (210+5 v w-3 (v^3) (w^3)))))))/(3 (v^9) (w^4) (((1+(v^2) (w^2)))^2)))-((2 (35+(v^4) (w^4)) ArcTan[v w])/((v^8) (w^3)))+((40 Log[2])/(3 (v^7) (w^2)))+((80 Log[v])/((v^7) (w^2)))+((80 Log[w])/((v^7) (w^2)))-((40 Log[1+(v^2) (w^2)])/((v^7) (w^2))),Derivative[4][bEF2][v_]->Derivative[3][bEF2v][v],Derivative[3][bEF2v][v_]->-((40 (D1a^2))/(3 (v^6)))-((16 D2a)/(v^5))-((4 π (w^2) (1+v w (4+v w (10+v w (20+v w (30+v w (36+v w (34+v w (40+v w (45+4 v w (10+v w (4+v w))))))))))))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-((16 D1a (5+v w (27+v w (85+v w (205+v w (395+v w (635+v w (877+v w (1045+v w (1055+v w (905+v w (675+v w (527+5 v w (77+3 v w (15+v w (5+v w))))))))))))))))/(3 (v^6) (((1+v w))^5) (((1+(v^2) (w^2)))^5)))+(1/(9 (v^6) (((-1+v w))^3) (((1+v w))^5) (((1+(v^2) (w^2)))^5)))4 (-240+v w (-444+v w (-645+v w (-846+v w (153+v w (964+v w (1787+v w (2610+v w (735+v w (-760+v w (-1133+3 v w (-502+v w (-827+v w (-732+v w (-25+11 v w (62+v w (9+2 v w (2+v w))))))))))))))))))+((8 w (3+v w (13+v w (34+v w (70+v w (113+v w (150+7 v w (24+v w (22+v w (19+v w (15+v w (10+v w (4+v w)))))))))))) ArcTan[v w])/(3 (v^5) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))+((8 (w^2) (-1+5 (v^4) (w^4) (1+5 (v^4) (w^4)+7 (v^8) (w^8))) Log[2])/(3 (v^4) (((-1+(v^4) (w^4)))^4)))+((64 (v^3) (w^9) (5+10 (v^4) (w^4)+(v^8) (w^8)) Log[v])/(3 (((-1+(v^4) (w^4)))^4)))+((64 (v^3) (w^9) (5+10 (v^4) (w^4)+(v^8) (w^8)) Log[w])/(3 (((-1+(v^4) (w^4)))^4)))-((8 (w^2) (1+v w (4+v w (10+v w (20+v w (30+v w (36+v w (34+v w (40+v w (45+4 v w (10+v w (4+v w))))))))))) Log[1+v w])/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-((4 (w^2) (-1+v w (4+v w (-10+v w (20+v w (-30+v w (36+v w (-34+v w (40+v w (-45+4 v w (10+v w (-4+v w))))))))))) Log[1+(v^2) (w^2)])/(3 (v^4) (((-1+v w))^4) (((1+(v^2) (w^2)))^4))),Derivative[3][dEF2][v_]->((8 D1a)/(v^5))+((4 (D1a^2))/(v^5))+((6 D2a)/(v^4))-((24+v w (66+v w (121+v w (189+v w (201+v w (173+3 v w (41+v w (17+3 v w (3+v w)))))))))/(3 (v^5) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((3 w ArcTan[v w])/(v^4)),Derivative[3][cEF2][v_]->-(1/2) Derivative[3][bEF2][v]+Derivative[3][dEF2][v]};

subsSOLo012DER4={Derivative[4][AEF0][v_]->-(840/((v^8) (w^4))),Derivative[4][AEF1][v_]->D1a ((16/(v^5))+(1120/((v^9) (w^4))))+(1120/((v^9) (w^4)))+(560/((v^8) (w^3))),Derivative[4][bEF1][v_]->-(32/(v^5))+((16 D1a)/(v^5))+((32 w)/(v^4))-((16 (w^2))/((v^3) (1+v w)))-((16 w (1+2 v w+3 (v^2) (w^2)))/((v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((16 (w^3))/((v^2)+(v^4) (w^2)))+((16 (w^2))/((v^3)+(v^5) (w^2)))-((16 w (1+3 v w+6 (v^2) (w^2)+18 (v^3) (w^3)+21 (v^4) (w^4)+15 (v^5) (w^5)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((8 w (1+4 v w+10 (v^2) (w^2)+16 (v^3) (w^3)+30 (v^4) (w^4)+60 (v^5) (w^5)+114 (v^6) (w^6)+96 (v^7) (w^7)+45 (v^8) (w^8)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4))),Derivative[4][cEF1][v_]->(16/(v^5))+((16 D1a)/(v^5))-((16 w)/(v^4))+((8 (w^2))/((v^3) (1+v w)))+((8 w (1+2 v w+3 (v^2) (w^2)))/((v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((8 (w^3))/((v^2)+(v^4) (w^2)))-((8 (w^2))/((v^3)+(v^5) (w^2)))+((8 w (1+3 v w+6 (v^2) (w^2)+18 (v^3) (w^3)+21 (v^4) (w^4)+15 (v^5) (w^5)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 w (1+4 v w+10 (v^2) (w^2)+16 (v^3) (w^3)+30 (v^4) (w^4)+60 (v^5) (w^5)+114 (v^6) (w^6)+96 (v^7) (w^7)+45 (v^8) (w^8)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4))),Derivative[4][AEF2][v_]->(40/(v^6))-(1008/((v^10) (w^4)))-(1120/((v^9) (w^3)))+(856/(3 (v^8) (w^2)))-((32 (w^6))/(((1+(v^2) (w^2)))^4))-((160 (w^4))/(3 (v^2) (((1+(v^2) (w^2)))^3)))-((100 (w^2))/((v^4) (((1+(v^2) (w^2)))^2)))-((80 (w^4))/(((v+(v^3) (w^2)))^2))-((400 (w^2))/((v^4)+(v^6) (w^2)))-(240/((v^6)+(v^8) (w^2)))-((16 (w^4) (1+(v^4) (w^4)))/((v^2) (((1+(v^2) (w^2)))^4)))-((56 (w^2) (1+(v^4) (w^4)))/((v^4) (((1+(v^2) (w^2)))^3)))-((152 (1+(v^4) (w^4)))/((v^6) (((1+(v^2) (w^2)))^2)))-((448 (1+(v^4) (w^4)))/((v^8) (w^2) (1+(v^2) (w^2))))-((16 D2a (70+(v^4) (w^4)))/((v^9) (w^4)))+((8 (D1a^2) (-378+5 (v^4) (w^4)))/(3 (v^10) (w^4)))+((136 (1+5 (v^4) (w^4)))/(3 (v^6) (((1+(v^2) (w^2)))^2)))+((16 D1a (-378-140 v w+15 (v^4) (w^4)))/(3 (v^10) (w^4)))+((168+840 (v^4) (w^4))/((v^8) (w^2)+(v^10) (w^4)))+((32 w (w+5 (v^4) (w^5)))/(3 (v^4) (((1+(v^2) (w^2)))^3)))+((8 (70+(v^4) (w^4)) ArcTan[v w])/((v^9) (w^3)))-((280 Log[2])/(3 (v^8) (w^2)))-((560 Log[v])/((v^8) (w^2)))-((560 Log[w])/((v^8) (w^2)))+((280 Log[1+(v^2) (w^2)])/((v^8) (w^2))),Derivative[5][bEF2][v_]->Derivative[4][bEF2v][v],Derivative[4][bEF2v][v_]->((80 (D1a^2))/(v^7))+((80 D2a)/(v^6))+((16 π (w^2) (1+5 v w+15 (v^2) (w^2)+35 (v^3) (w^3)+65 (v^4) (w^4)+101 (v^5) (w^5)+135 (v^6) (w^6)+140 (v^7) (w^7)+115 (v^8) (w^8)+85 (v^9) (w^9)+101 (v^10) (w^10)+105 (v^11) (w^11)+75 (v^12) (w^12)+25 (v^13) (w^13)+5 (v^14) (w^14)))/(3 (v^5) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))+(1/(3 (v^7) (((1+v w))^6) (((1+(v^2) (w^2)))^6)))160 D1a (3+19 v w+69 (v^2) (w^2)+189 (v^3) (w^3)+416 (v^4) (w^4)+768 (v^5) (w^5)+1224 (v^6) (w^6)+1704 (v^7) (w^7)+2100 (v^8) (w^8)+2301 (v^9) (w^9)+2218 (v^10) (w^10)+1809 (v^11) (w^11)+1260 (v^12) (w^12)+810 (v^13) (w^13)+576 (v^14) (w^14)+378 (v^15) (w^15)+189 (v^16) (w^16)+54 (v^17) (w^17)+9 (v^18) (w^18))-(1/(9 (v^7) (((-1+v w))^4) (((1+v w))^6) (((1+(v^2) (w^2)))^6)))8 (720+1350 v w+1965 (v^2) (w^2)+2580 (v^3) (w^3)-1122 (v^4) (w^4)-4274 (v^5) (w^5)-7345 (v^6) (w^6)-10416 (v^7) (w^7)-2994 (v^8) (w^8)+2868 (v^9) (w^9)+11004 (v^10) (w^10)+19140 (v^11) (w^11)+1518 (v^12) (w^12)-8704 (v^13) (w^13)-2516 (v^14) (w^14)+3672 (v^15) (w^15)-13614 (v^16) (w^16)-13842 (v^17) (w^17)-2505 (v^18) (w^18)+8832 (v^19) (w^19)+900 (v^20) (w^20)+330 (v^21) (w^21)+165 (v^22) (w^22))-((8 w (15+79 v w+245 (v^2) (w^2)+585 (v^3) (w^3)+1115 (v^4) (w^4)+1775 (v^5) (w^5)+2429 (v^6) (w^6)+2865 (v^7) (w^7)+2885 (v^8) (w^8)+2485 (v^9) (w^9)+1855 (v^10) (w^10)+1379 (v^11) (w^11)+945 (v^12) (w^12)+525 (v^13) (w^13)+175 (v^14) (w^14)+35 (v^15) (w^15)) ArcTan[v w])/(3 (v^6) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))-((32 ((w^2)-5 (v^4) (w^6)+45 (v^8) (w^10)+145 (v^12) (w^14)+70 (v^16) (w^18)) Log[2])/(3 (v^5) (((-1+(v^4) (w^4)))^5)))-((64 (v^2) (w^9) (15+135 (v^4) (w^4)+101 (v^8) (w^8)+5 (v^12) (w^12)) Log[v])/(3 (((-1+(v^4) (w^4)))^5)))-((64 (v^2) (w^9) (15+135 (v^4) (w^4)+101 (v^8) (w^8)+5 (v^12) (w^12)) Log[w])/(3 (((-1+(v^4) (w^4)))^5)))+((32 (w^2) (1+5 v w+15 (v^2) (w^2)+35 (v^3) (w^3)+65 (v^4) (w^4)+101 (v^5) (w^5)+135 (v^6) (w^6)+140 (v^7) (w^7)+115 (v^8) (w^8)+85 (v^9) (w^9)+101 (v^10) (w^10)+105 (v^11) (w^11)+75 (v^12) (w^12)+25 (v^13) (w^13)+5 (v^14) (w^14)) Log[1+v w])/(3 (v^5) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))+((16 (w^2) (1-5 v w+15 (v^2) (w^2)-35 (v^3) (w^3)+65 (v^4) (w^4)-101 (v^5) (w^5)+135 (v^6) (w^6)-140 (v^7) (w^7)+115 (v^8) (w^8)-85 (v^9) (w^9)+101 (v^10) (w^10)-105 (v^11) (w^11)+75 (v^12) (w^12)-25 (v^13) (w^13)+5 (v^14) (w^14)) Log[1+(v^2) (w^2)])/(3 (v^5) (((-1+v w))^5) (((1+(v^2) (w^2)))^5))),Derivative[4][dEF2][v_]->(40/(v^6))-((40 D1a)/(v^6))-((20 (D1a^2))/(v^6))-((24 D2a)/(v^5))-((8 w)/(v^5))-((8 (w^2))/(v^4))-((6 (w^4))/((v^2) (((1+v w))^2)))+((8 (w^3))/((v^3) (1+v w)))-((36 (w^6))/(((1+(v^2) (w^2)))^2))+((12 (w^4) (-3+v w))/(((v+(v^3) (w^2)))^2))+((42 (w^4))/((v^2)+(v^4) (w^2)))-((12 (w^3))/((v^3)+(v^5) (w^2)))+((4 (w^2) (-3+v w))/((v^4)+(v^6) (w^2)))+((32 (w^2) (1+3 v w+6 (v^2) (w^2)+5 (v^3) (w^3)+3 (v^4) (w^4)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 (w^2) (1+4 v w+10 (v^2) (w^2)+30 (v^3) (w^3)+53 (v^4) (w^4)+68 (v^5) (w^5)+44 (v^6) (w^6)+18 (v^7) (w^7)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))+((12 w ArcTan[v w])/(v^5)),Derivative[4][cEF2][v_]->-(1/2) Derivative[4][bEF2][v]+Derivative[4][dEF2][v]};

subsSOLbEF2={bEF2[v_]->(8/(9 (v^2)))-((2 D1a)/(9 (v^2)))-((D1a^2)/(9 (v^2)))-((2 D2a)/(3 v))-((2 w)/(3 v))-((4 D1a w)/(9 v))+((Catalan (w^2))/9)+((π (w^2))/9)+((7/216)-((11 I)/432)) (π^2) (w^2)-((2 (w^2))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))-((2 v (w^3))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((2 (v^2) (w^4))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((4 D1a (v^2) (w^4))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((w ArcTan[v w])/(3 v))-(2/9) (w^2) ArcTan[v w]+((1/9)+(I/18)) π (w^2) ArcTan[v w]-((1/9)-(I/9)) (w^2) ((ArcTan[v w])^2)-(5/36) π (w^2) Log[2]+(1/18) (w^2) ((Log[2])^2)-(10/9) (w^2) Log[v]+(4/9) (w^2) Log[2] Log[v]-(10/9) (w^2) Log[w]+((5/18)-((2 I)/9)) π (w^2) Log[w]-(2/3) (w^2) ArcTan[v w] Log[w]+(4/9) (w^2) ArcTan[((-1+v w)/(1+v w))] Log[w]+((4/9)-(I/9)) (w^2) Log[2] Log[w]-(2/9) (w^2) Log[v] Log[1-v w]-(1/9) I (w^2) Log[w] (-Log[2]+Log[1-I v w])-(1/9) (w^2) Log[2] Log[-1+v w]-(2/9) (w^2) Log[w] Log[-1+v w]+(1/9) π (w^2) (-((I π)/2)+Log[2]-Log[-I+v w])-(4/9) (w^2) ArcTan[v w] (Log[2]+Log[v]+Log[w]-Log[I+v w])+(1/9) I (w^2) Log[2] Log[I+v w]-(4/9) I (w^2) Log[v] Log[I+v w]-(1/9) I (w^2) Log[w] Log[I+v w]-(1/9) (w^2) (-Log[2]+Log[1-I v w]) Log[I+v w]-(2/9) (w^2) Log[-1+v w] Log[I+v w]+(2/9) (w^2) (Log[-(1/2)+(I/2)]+Log[-1+v w]) Log[I+v w]+(1/18) (w^2) ((Log[I+v w])^2)+(2/9) (w^2) Log[1+v w]-(1/9) π (w^2) Log[1+v w]+(1/9) I (w^2) Log[2] Log[1+v w]+(2/9) (w^2) Log[v] Log[1+v w]+(2/9) (w^2) Log[w] Log[1+v w]+(2/9) I (w^2) (Log[-(1/2)-(I/2)]+Log[I+v w]) Log[1+v w]-(1/9) (w^2) ((Log[1+v w])^2)+(1/18) π (w^2) (Log[1+I]-Log[I+v w]+Log[1+v w])+(2/9) (w^2) ArcTan[v w] (Log[1+I]-Log[I+v w]+Log[1+v w])+(4/9) (w^2) Log[1+(v^2) (w^2)]-(2/9) (w^2) Log[2] Log[1+(v^2) (w^2)]+(2/9) I (w^2) Log[v] Log[1+(v^2) (w^2)]+(1/9) I (w^2) Log[w] Log[1+(v^2) (w^2)]+((1/18)+(I/18)) (w^2) (-Log[2]+Log[1-I v w]) Log[1+(v^2) (w^2)]+(2/9) (w^2) Log[-1+v w] Log[1+(v^2) (w^2)]-(1/9) (w^2) (Log[-(1/2)+(I/2)]+Log[-1+v w]) Log[1+(v^2) (w^2)]-((1/9)+(I/9)) (w^2) Log[1+v w] Log[1+(v^2) (w^2)]+((1/36)-(I/36)) (w^2) ((Log[1+(v^2) (w^2)])^2)-(1/18) π (w^2) Log[Sin[(π/4)+ArcTan[v w]]]-(2/9) (w^2) PolyLog[2,-v w]+((2/9)+((2 I)/9)) (w^2) PolyLog[2,-I v w]+((2/9)-((2 I)/9)) (w^2) PolyLog[2,I v w]-(2/9) (w^2) PolyLog[2,v w]+((1/18)-(I/18)) (w^2) PolyLog[2,(1/2)-((I v w)/2)]+((1/18)+(I/18)) (w^2) PolyLog[2,(1/2)+((I v w)/2)]+(1/9) (w^2) PolyLog[2,((1/2)+(I/2)) (-I+v w)]+(2/9) I (w^2) PolyLog[2,((I-v w)/(I+v w))]-(1/9) I (w^2) PolyLog[2,-((1+I v w)/(I+v w))]+(1/9) (w^2) PolyLog[2,((1/2)-(I/2)) (I+v w)]-((1/9)+(I/9)) (w^2) PolyLog[2,((1/2)-(I/2)) (1+v w)]-((1/9)-(I/9)) (w^2) PolyLog[2,((1/2)+(I/2)) (1+v w)]};

subsSOLo012wDERupto4=Union[subsSOLo012,subsSOLo012DER1,subsSOLo012DER2,subsSOLo012DER3,subsSOLo012DER4];

SOLcheck up to 2 order

eqn1o0//.subsSOLo012wDERupto4//Simplify

eqn2o0//.subsSOLo012wDERupto4//Simplify

eqn3o0//.subsSOLo012wDERupto4//Simplify

eqn4o0//.subsSOLo012wDERupto4//Simplify

eqn5o0//.subsSOLo012wDERupto4//Simplify

eqn1o1//.subsSOLo012wDERupto4//Simplify

eqn2o1//.subsSOLo012wDERupto4//Simplify

eqn3o1//.subsSOLo012wDERupto4//Simplify

eqn4o1//.subsSOLo012wDERupto4//Simplify

eqn5o1//.subsSOLo012wDERupto4//Simplify

eqn1o2//.subsSOLo012wDERupto4//Simplify

eqn2o2//.subsSOLo012wDERupto4//Simplify

eqn3o2//.subsSOLo012wDERupto4//Simplify

eqn4o2//.subsSOLo012wDERupto4//Simplify

eqn5o2//.subsSOLo012wDERupto4//Simplify

Simplify/@Series[D[bEF2[v]//.subsSOLbEF2,v]-(bEF2'[v]//.subsSOLo012wDERupto4),{v,∞,30}]//N//Chop

Simplify/@Series[bEF2[v]//.subsSOLbEF2,{v,∞,10}]//N//Chop

All functions up to the second order solve Einstein equations. Moreover integrate bEF2v[v] is real, as it has to be

3 ORDER

INITIAL PROCEDURES

cEF3[v_]=dEF3[v]-(1/2)bEF3[v];

subsallo3ZERO={AEF3[v]->0,AEF3'[v]->0,AEF3''[v]->0,bEF3[v]->0,bEF3'[v]->0,bEF3''[v]->0,dEF3[v]->0,dEF3'[v]->0,dEF3''[v]->0};

subsallo3LIST={AEF3[v],AEF3'[v],AEF3''[v],bEF3[v],bEF3'[v],bEF3''[v],dEF3[v],dEF3'[v],dEF3''[v]};

Third order Einstein equation' s dependence on third order functions :

form1o3=Simplify/@Collect[(eqn1o3-(eqn1o3//.subsallo3ZERO))//.subsSOLo012wDERupto4//Expand,subsallo3LIST]

form2o3=Simplify/@Collect[(eqn2o3-(eqn2o3//.subsallo3ZERO))//.subsSOLo012wDERupto4//Expand,subsallo3LIST]

form3o3=Simplify/@Collect[(eqn3o3-(eqn3o3//.subsallo3ZERO))//.subsSOLo012wDERupto4//Expand,subsallo3LIST]

form4o3=Simplify/@Collect[(eqn4o3-(eqn4o3//.subsallo3ZERO))//.subsSOLo012wDERupto4//Expand,subsallo3LIST]

form5o3=Simplify/@Collect[(eqn5o3-(eqn5o3//.subsallo3ZERO))//.subsSOLo012wDERupto4//Expand,subsallo3LIST]

Eqns 4 and 5 are linearly dependent, so they are only 4 independent Eqns : 1, 2, 3, 4. Here is a proof:

Simplify/@Collect[(1/(D[form5o3,AEF3''[v]]))form5o3-(1/(D[form4o3,AEF3''[v]]))form4o3,subsallo3LIST]

(Collect[(1/(D[form5o3,AEF3''[v]]))eqn5o3-(1/(D[form4o3,AEF3''[v]]))eqn4o3,subsallo3LIST]//.subsSOLo012wDERupto4)//Simplify

Analogous equation can be found in the fourth order.

CONSTRo4=(Collect[(1/(D[eqn5o4,AEF4''[v]]))eqn5o4-(1/(D[eqn4o4,AEF4''[v]]))eqn4o4,subsallo3LIST])//Expand

D[CONSTRo4,AEF4[v]]//.subsSOLo012wDERupto4//Simplify

It does not depend on the functions from the fourth order :

(CONSTRo4-(CONSTRo4//.{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0,bEF4[v]->0,bEF4'[v]->0,bEF4''[v]->0,cEF4[v]->0,cEF4'[v]->0,cEF4''[v]->0}))//.subsSOLo012wDERupto4//Expand//Simplify

subsCOMBO - general utility for substitutions

Various substitutions used later on are gathered in subsCOMBO list :

subsCOMBO={Log[ah_Integer]->xxx[ah],Log[ah_Complex]->Log[Abs[ah]]+I Arg[ah],(E^(2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)+I 2Sin[ah]Cos[ah],(E^(-2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)-I 2Sin[ah]Cos[ah],Log[Times[ah_,bh_]]->Log[ah]+Log[bh],Log[Times[ah_,bh_,ch_]]->Log[ah]+Log[bh]+Log[ch],Log[(1/(ah_))]->-Log[ah],

Log[v-(I/w)]->Log[v w-I]-Log[w],Log[v+(I/w)]->Log[v w+I]-Log[w],Log[v w-I]->Log[1+(v^2)(w^2)]-Log[I+v w],Log[1-((1/2)-(I/2)) (1+v w)]->Log[1+(v^2)(w^2)]-Log[1-((1/2)+(I/2)) (1+v w)]-Log[2],Log[1+I v w]->Log[I]+Log[-I+v w],Log[1-I v w]->Log[-I]+Log[I+v w],Log[1-((1/2)+(I/2)) (v-(I/w)) w]->2Log[-1+v w]-Log[2]-Log[1-((1/2)-(I/2)) (v+(I/w)) w],
Log[((v w)/(Sqrt[1+(v^2) (w^2)]))]->Log[v]+Log[w]-(1/2)Log[1+(v^2)(w^2)],Log[-1+(v^4) (w^4)]->Log[-1+v w]+Log[1+v w]+Log[1+(v^2)(w^2)],Log[1+(1/2) I (v+(I/w)) w]->Log[1+(v^2)(w^2)]-Log[4]-Log[1-(1/2) I (v-(I/w)) w],Log[1-v w]->I π+Log[-1+v w],Log[(1+I)-(1-I) v w]->Log[2]+Log[1+(v^2)(w^2)]-Log[(1-I)-(1+I) v w],ArcTan[((1+v w)/(1-v w))]->ArcTan[((-1+v w)/(1+v w))]-(π/2),ArcTan[((1+v w)/(-1+v w))]->-ArcTan[((-1+v w)/(1+v w))]+(π/2),ArcTan[((1-v w)/(1+v w))]->-ArcTan[((-1+v w)/(1+v w))],
Log[(1-I)-(1+I)v w]->Log[1+I]+Log[I+v w]-I π,Log[((1/2)+(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[-1+v w],Log[((1/2)-(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-1+v w],Log[v-(1/w)]->Log[-1+v w]-Log[w],Log[((1/2)-(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[I+v w],Log[((1/2)+(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[1+v w],Log[((1/2)+(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[I+v w],Log[((1/2)-(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[-I+v w],Log[((1/2)+(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-I+v w],Log[((1/2)-(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[1+v w],Log[1-(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))+(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[v]+Log[w]-Log[I+v w],Log[1-I ((1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2))))]->Log[1+I]+Log[1+v w]-Log[I+v w],Log[1+(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[I]-I π-Log[-I+v w],Log[v+(1/w)]->Log[1+v w]-Log[w],Log[1-(1/2) I (v-(I/w)) w]->-Log[2]+Log[I+v w]-I (π/2),Log[1+((1/2)+(I/2)) (I+v w)]->Log[(1/2)+(I/2)]+Log[1+v w],Log[1-((1/2)+(I/2)) (1+v w)]->Log[(1/2)+(I/2)]+Log[I+v w]-I π,Log[1+(1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+I (π/2)-Log[I+v w],Log[(((1+v w))^2)]->2Log[1+v w], Log[-1+(v^2) (w^2)]->Log[-1+v w]+Log[1+v w]};

test of subsCOMBO

Simplify/@Series[Drop[subsCOMBO,7]//.Rule[ah_,bh_]->ah-bh,{v,∞,50}]//N//Chop

IT WORKS!!!

dEF3v[v]

DSolve[(form1o3+eqn1o3REST[v]//.{dEF3'[v]->dEF3v[v],dEF3''[v]->dEF3v'[v]})==0,dEF3v[v],v]

eqn1o3REST[v_]=(eqn1o3-form1o3//Expand)//.subsSOLo012wDERupto4//Simplify;

dEF3vNEW[v_]=Simplify/@Collect[Expand[((D3a-(I/3) π (w^2) Log[w])/(v^2))+(1/(v^2))(Expand[Integrate[#,v]&/@(Simplify/@Collect[eqn1o3REST[v] (v^2)//.Log[ah_Integer]->xxx[ah],{D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a ArcTan[ah_],D1a,D2a,Log[ah_],π}])]//.subsCOMBO)],{D1a D2a,D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}];

dEF3vNEW[v] satisfies Einstein EQNS :

Simplify/@(Series[eqn1o3//.Union[subsSOLo012wDERupto4,{dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]}]//Expand,{v,∞,30}]//.subsCOMBO)

and is regular at v = (1/w) (no Log divergence)

Simplify/@(Assuming[And[v>0,v>(1/w)],Series[dEF3vNEW[v],{v,(1/w),1}]]//.subsCOMBO)

dEF3[v]

dEF3NEW[v_]=-(-((Catalan (w^3))/18)+((37/288)+((421 I)/576)) π (w^3)-((13/432)-(I/32)) (π^2) (w^3)-((17/72)+(I/72)) π (w^3) Log[2]-(1/36) (w^3) ((Log[2])^2)+(5/12) (w^3) Log[w]+((5/12)+(I/18)) π (w^3) Log[w]-((2/9)-(I/6)) (w^3) Log[2] Log[w]-((23/36)+((2 I)/3)) (w^3) ((Log[w])^2))+(Simplify/@Collect[Expand[(Integrate[#,v]&/@dEF3vNEW[v])//.subsCOMBO],{D1a D2a,D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}]);

Simplify/@(Series[dEF3NEW[v],{v,∞,10}]//.subsCOMBO)

(Simplify/@Series[D[dEF3NEW[v],v]-dEF3vNEW[v],{v,∞,15}])//N//Chop

SeriesCoefficient[Simplify/@(Series[dEF3NEW[v],{v,∞,1}]//.subsCOMBO),0]//Expand

A3old[v]

(D[form3o3+(1/2)form2o3//Expand,dEF3''[v]]form1o3+form3o3+(1/2)form2o3)//Expand

DSolve[-6 (v^2) AEF3[v]-(3/2) (v^3) AEF3'[v]+eqn4A3REST[v]==0,AEF3[v],v]

form1o3

eqn4A3REST[v_]=Expand[D[form3o3+(1/2)form2o3//Expand,dEF3''[v]]eqn1o3+eqn3o3+(1/2)eqn2o3]//.{AEF3[v]->0,AEF3'[v]->0};

AEF3NEW[v_]=Simplify/@Collect[Expand[((AEF3a/(v^4))+(1/(v^4))(Integrate[#,v]&/@(Simplify/@Collect[(Expand[(2/3)v eqn4A3REST[v]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{dEF3'[v]->dEF3vNEW[v]}]]//Simplify)//.subsCOMBO,Union[subsallo3LIST,{Catalan,D1a D2a,D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}]])))//.subsCOMBO],{D1a D2a,D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}];

Simplify/@((Simplify/@Series[Expand[eqn1o3]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]}],{v,∞,15}])//.subsCOMBO)

Simplify/@((Simplify/@Series[Expand[eqn4o3]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]}],{v,∞,15}])//.Union[subsCOMBO,{Floor[((Arg[(1/(I+v w))])/(2 π))]->-1}])

Simplify/@((Simplify/@Series[Expand[(1/(D[form2o3,bEF3''[v]]))eqn2o3-(1/(D[form3o3,bEF3''[v]]))eqn3o3]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v],bEF3[v]->0,bEF3'[v]->0,bEF3''[v]->0}],{v,∞,15}])//.Union[subsCOMBO,{Floor[((Arg[(1/(I+v w))])/(2 π))]->-1}])

b3v[v]

bEF3vTOEVAL[v_]=Expand[bEF3'[v]/.Union[Flatten[Solve[CONSTRo4==0,bEF3'[v]]],{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0}]];

((Simplify/@Collect[(Simplify/@Expand[bEF3vTOEVAL[v]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]},{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0}]])//.subsCOMBO,{Catalan,AEF3a D1a,AEF3a,D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a Log[ah_],D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}])//.{Log[ah_]->0,ArcTan[ah_]->0,Catalan->0,π->0,D1a->0,D2a->0,D3a->0,AEF3a->0,PolyLog[2,ah_]->0})//FullSimplify

bEF3vBYPRODUCT[v_]=-((208+v w (384+v w (564+v w ((642+117 I)+v w ((88+234 I)+v w ((-252+351 I)+v w ((-656+468 I)+v w ((-952+351 I)+v w ((-432+234 I)+v w ((-156+117 I)+2 v w (-6+31 v w)))))))))))/(108 (v^4) (-1+v w) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+(Simplify/@Collect[Expand[(Simplify/@Collect[(Simplify/@Expand[bEF3vTOEVAL[v]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]},{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0}]])//.subsCOMBO,{Catalan,AEF3a D1a,AEF3a,D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a Log[ah_],D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}])-((Simplify/@Collect[(Simplify/@Expand[bEF3vTOEVAL[v]//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]},{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0}]])//.subsCOMBO,{Catalan,AEF3a D1a,AEF3a,D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a Log[ah_],D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}])//.{Log[ah_]->0,ArcTan[ah_]->0,Catalan->0,π->0,D1a->0,D2a->0,D3a->0,AEF3a->0,PolyLog[2,ah_]->0})],
{Catalan,AEF3a D1a,AEF3a,D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a Log[ah_],D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}
]);

//.Flatten[Solve[SeriesCoefficient[Simplify/@(Assuming[v>(1/w),Series[bEF3vBYPRODUCT[v],{v,(1/w),1}]]//.subsCOMBO),-1]==0,AEF3a]//Simplify//Expand];

(Simplify/@Series[eqn2o3//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v]},{bEF3[v]->0,bEF3'[v]->bEF3vNEW[v],bEF3''[v]->bEF3vNEW'[v]}],{v,∞,20}]//.Floor[((Arg[(1/(I+v w))])/(2 π))]->-1)//N//Chop

bEF3vNEW[v_]=bEF3vBYPRODUCT[v]

AEF3a=-(((7/81)-((13 I)/72))/w)+((2 I Catalan)/(9 w))-((((59/432)-(I/9)) π)/w)+((((11/216)-(I/36)) (π^2))/w)+((((2/81)-(I/72)) Log[2])/w)+((((25/54)+(I/9)) π Log[2])/w)+((((17/324)-(I/18)) ((Log[2])^2))/w)-((2 Log[w])/(9 w))-((((1/18)+(I/6)) π Log[w])/w)+((((1/3)-(I/9)) Log[2] Log[w])/w)+((((4/9)+((4 I)/9)) ((Log[w])^2))/w)+((((1/81)+((2 I)/81)) PolyLog[2,(1/2)-(I/2)])/w)+((((1/81)-((2 I)/81)) PolyLog[2,(1/2)+(I/2)])/w)+((((17/162)+((7 I)/81)) PolyLog[2,1-I])/w)-((((19/162)-((11 I)/81)) PolyLog[2,1+I])/w);

(Simplify/@(Series[bEF3vNEW[v],{v,∞,15}]//.Union[{Floor[((Arg[(1/(I+v w))])/(2 π))]->-1},subsCOMBO]))//N//Chop

Assuming[And[v>(1/w),v∈Reals,w>0],Series[Simplify/@Collect[Expand[(Simplify/@Expand[CONSTRo4//.Union[subsSOLo012wDERupto4,subsSOLbEF2,{AEF4[v]->0,AEF4'[v]->0,AEF4''[v]->0,bEF4[v]->0,bEF4'[v]->0,bEF4''[v]->0,cEF4[v]->0,cEF4'[v]->0,cEF4''[v]->0},{AEF3[v]->AEF3NEW[v],AEF3'[v]->AEF3NEW'[v],AEF3''[v]->AEF3NEW''[v],dEF3[v]->dEF3NEW[v],dEF3'[v]->dEF3vNEW[v],dEF3''[v]->dEF3vNEW'[v],bEF3'[v]->bEF3vNEW[v]}]])//.subsCOMBO],{Catalan,AEF3a D1a,AEF3a,D1a D2a,D1a Log[ah_],D2a Log[ah_],D1a ArcTan[ah_],D2a Log[ah_],D1a,D2a,Log[ah_]Log[bh_],ArcTan[ah_]Log[bh_],π Log[ah_],Log[ah_],ArcTan[bh_],PolyLog[2,ch_],π}],{v,∞,20}]]//.Floor[((Arg[(1/(I+v w))])/(2 π))]->-1

FG PART

Quit[];

Einstein EQNS in EF coordinates

coord = {z,τ,y,x1,x2};

metricsign=-1;

$Assumptions= And[τ∈Reals,x1∈Reals,x2∈Reals,r∈Reals,th1∈Reals,th2∈Reals,th3∈Reals,th4∈Reals,th5∈Reals,z>0,w>0];

metric=(({{(1/(z^2)), 0, 0, 0, 0}, {0, -(1/(z^2))Exp[aFG[τ,z]], 0, 0, 0}, {0, 0, (1/(z^2))(τ^2) Exp[bFG[τ,z]], 0, 0}, {0, 0, 0, (1/(z^2))Exp[cFG[τ,z]], 0}, {0, 0, 0, 0, (1/(z^2))Exp[cFG[τ,z]]}}));

<<diffgeo.m

einsteinEqnsFG=Union[Flatten[RicciTensor+4 metric]];

eqnFG1=Expand[einsteinEqnsFG[[2]]];
eqnFG2=Expand[einsteinEqnsFG[[3]]];
eqnFG3=Expand[einsteinEqnsFG[[4]]];
eqnFG4=Expand[einsteinEqnsFG[[5]]];
eqnFG5=Expand[einsteinEqnsFG[[6]]];

einsteinEqns=Union[Flatten[RicciTensor+4 metric]];

aFG[τ_,z_]:=aFG0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))aFG1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))aFG2[(z/(τ^(1/3)))]+(1/(τ^2))aFG3[(z/(τ^(1/3)))];
bFG[τ_,z_]:=bFG0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))bFG1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))bFG2[(z/(τ^(1/3)))]+(1/(τ^2))bFG3[(z/(τ^(1/3)))];
cFG[τ_,z_]:=cFG0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))cFG1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))cFG2[(z/(τ^(1/3)))]+(1/(τ^2))cFG3[(z/(τ^(1/3)))];

eqnFG1S=Expand/@Series[Expand[(u^(-1))eqnFG1//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,3}];
eqnFG2S=Expand/@Series[Expand[(u^(-2))eqnFG2//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,3}];
eqnFG3S=Expand/@Series[Expand[(u^2)eqnFG3//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,3}];
eqnFG4S=Expand/@Series[Expand[(u^(-1))eqnFG4//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,3}];
eqnFG5S=Expand/@Series[Expand[(u^(-1))eqnFG5//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh))}],{u,0,3}];

eqnFG1o0=SeriesCoefficient[eqnFG1S,0];
eqnFG1o1=SeriesCoefficient[eqnFG1S,1];
eqnFG1o2=SeriesCoefficient[eqnFG1S,2];
eqnFG1o3=SeriesCoefficient[eqnFG1S,3];

eqnFG2o0=SeriesCoefficient[eqnFG2S,0];
eqnFG2o1=SeriesCoefficient[eqnFG2S,1];
eqnFG2o2=SeriesCoefficient[eqnFG2S,2];
eqnFG2o3=SeriesCoefficient[eqnFG2S,3];

eqnFG3o0=SeriesCoefficient[eqnFG3S,0];
eqnFG3o1=SeriesCoefficient[eqnFG3S,1];
eqnFG3o2=SeriesCoefficient[eqnFG3S,2];
eqnFG3o3=SeriesCoefficient[eqnFG3S,3];

eqnFG4o0=SeriesCoefficient[eqnFG4S,0];
eqnFG4o1=SeriesCoefficient[eqnFG4S,1];
eqnFG4o2=SeriesCoefficient[eqnFG4S,2];
eqnFG4o3=SeriesCoefficient[eqnFG4S,3];

eqnFG5o0=SeriesCoefficient[eqnFG5S,0];
eqnFG5o1=SeriesCoefficient[eqnFG5S,1];
eqnFG5o2=SeriesCoefficient[eqnFG5S,2];
eqnFG5o3=SeriesCoefficient[eqnFG5S,3];

Procedure xxx[ch] simplifies logarithms of integer numbers

xxx[ch_Integer]:=FactorInteger[ch]/.{List[ah_Integer,bh_Integer]->bh Log[ah],List->Plus}

SOLUTIONS IN FG coordinates

subsSOLFG={
aFG0[v]->2Log[(3^(1/4))+v]+2Log[(3^(1/4))-v]+2Log[(3^(1/2))+(v^2)]-Log[3+(v^4)]-Log[3],
bFG0[v]->Log[3+(v^4)]-Log[3],
cFG0[v]->Log[3+(v^4)]-Log[3],

aFG1[v]->(((Sqrt[2]) (v^4) (9+(v^4)))/((3^(3/4)) (9-(v^8)))),
bFG1[v]->-(((Sqrt[2]) (v^4))/((3^(3/4)) (3+(v^4))))+(((Sqrt[2]) Log[(3^(1/4))-v])/(3^(3/4)))+(((Sqrt[2]) Log[(3^(1/4))+v])/(3^(3/4)))+(((Sqrt[2]) Log[(Sqrt[3])+(v^2)])/(3^(3/4)))-(((Sqrt[2]) Log[3+(v^4)])/(3^(3/4))),
cFG1[v]->-(((Sqrt[2]) (v^4))/((3^(3/4)) (3+(v^4))))-((Log[(3^(1/4))-v])/((Sqrt[2]) (3^(3/4))))-((Log[(3^(1/4))+v])/((Sqrt[2]) (3^(3/4))))-((Log[(Sqrt[3])+(v^2)])/((Sqrt[2]) (3^(3/4))))+((Log[3+(v^4)])/((Sqrt[2]) (3^(3/4)))),

aFG2[v]->-(((v^2) (-486+243 (Sqrt[3]) (v^2)-270 (v^4)+63 (Sqrt[3]) (v^6)+54 (v^8)+45 (Sqrt[3]) (v^10)+30 (v^12)+(Sqrt[3]) (v^14)))/(36 (((-9+(v^8)))^2)))+(((v^4) (9+(v^4)) Log[2])/(6 (Sqrt[3]) (-9+(v^8))))-((Log[(Sqrt[3])+(v^2)])/(2 (Sqrt[3])))+((Log[3+(v^4)])/(4 (Sqrt[3]))),

bFG2[v]->((π^2)/(72 (Sqrt[3])))-(((v^2) (-162+171 (Sqrt[3]) (v^2)-144 (v^4)+36 (Sqrt[3]) (v^6)-30 (v^8)+(Sqrt[3]) (v^10)))/(36 (-3+(v^4)) (((3+(v^4)))^2)))-((ArcTanh[((v^2)/(Sqrt[3]))])/(2 (Sqrt[3])))+(((v^4) Log[2])/((Sqrt[3]) (18+6 (v^4))))+((Log[(3^(1/4))-v])/(12 (Sqrt[3])))-(((Log[(3^(1/4))-v])^2)/(6 (Sqrt[3])))+((Log[(3^(1/4))+v])/(12 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[(3^(1/4))+v])/(3 (Sqrt[3])))-(((Log[(3^(1/4))+v])^2)/(6 (Sqrt[3])))+((13 Log[(Sqrt[3])+(v^2)])/(12 (Sqrt[3])))-((2 Log[2] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))-((Log[(3^(1/4))+v] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))+(((Log[(Sqrt[3])+(v^2)])^2)/(2 (Sqrt[3])))-((7 Log[3+(v^4)])/(12 (Sqrt[3])))+((Log[2] Log[3+(v^4)])/(3 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[3+(v^4)])/(3 (Sqrt[3])))+((Log[(3^(1/4))+v] Log[3+(v^4)])/(3 (Sqrt[3])))-((Log[(Sqrt[3])+(v^2)] Log[3+(v^4)])/(3 (Sqrt[3])))+((PolyLog[2,-((((-3+(Sqrt[3]) (v^2)))^2)/(((3+(Sqrt[3]) (v^2)))^2))])/(6 (Sqrt[3]))),

cFG2[v]->-((π^2)/(144 (Sqrt[3])))-(((v^2) (162-45 (Sqrt[3]) (v^2)+72 (v^4)-36 (Sqrt[3]) (v^6)+6 (v^8)+(Sqrt[3]) (v^10)))/(36 (-3+(v^4)) (((3+(v^4)))^2)))+(((v^4) Log[2])/((Sqrt[3]) (18+6 (v^4))))+((Log[(3^(1/4))-v])/(12 (Sqrt[3])))+(((Log[(3^(1/4))-v])^2)/(12 (Sqrt[3])))+((Log[(3^(1/4))+v])/(12 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[(3^(1/4))+v])/(6 (Sqrt[3])))+(((Log[(3^(1/4))+v])^2)/(12 (Sqrt[3])))-((5 Log[(Sqrt[3])+(v^2)])/(12 (Sqrt[3])))+((Log[2] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[(Sqrt[3])+(v^2)])/(6 (Sqrt[3])))+((Log[(3^(1/4))+v] Log[(Sqrt[3])+(v^2)])/(6 (Sqrt[3])))-(((Log[(Sqrt[3])+(v^2)])^2)/(4 (Sqrt[3])))+((Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[2] Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[(3^(1/4))+v] Log[3+(v^4)])/(6 (Sqrt[3])))+((Log[(Sqrt[3])+(v^2)] Log[3+(v^4)])/(6 (Sqrt[3])))-((PolyLog[2,-((((-3+(Sqrt[3]) (v^2)))^2)/(((3+(Sqrt[3]) (v^2)))^2))])/(12 (Sqrt[3])))
};

Third order functions taken from [hep - th/0703243]

aFG3vNEW[v_]=-((DFG3a (v^3) (9+2 (v^4)+(v^8)))/(((-9+(v^8)))^2))+((2 (Sqrt[2]) (v^3) (4374 (Sqrt[3])-9477 (v^2)+1458 (Sqrt[3]) (v^4)-3402 (v^6)+1944 (Sqrt[3]) (v^8)-1053 (v^10)+432 (Sqrt[3]) (v^12)+108 (v^14)+594 (Sqrt[3]) (v^16)+225 (v^18)+30 (Sqrt[3]) (v^20)+30 (v^22)+(v^26)))/(3 (3^(3/4)) (((-9+(v^8)))^4)))+((8 (Sqrt[2]) (v^3) (9+2 (v^4)+(v^8)) ArcTan[((v^2)/(Sqrt[3]))])/((3^(1/4)) (((-9+(v^8)))^2)))-((8 (Sqrt[2]) (v^7) (9+18 (v^4)+(v^8)) Log[2])/((3^(1/4)) (((-9+(v^8)))^3)))+(((Sqrt[2]) v (-45+18 (Sqrt[3]) (v^2)-6 (v^4)+6 (Sqrt[3]) (v^6)-5 (v^8)) Log[(3^(1/4))-v])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))+(((Sqrt[2]) v (-45+18 (Sqrt[3]) (v^2)-6 (v^4)+6 (Sqrt[3]) (v^6)-5 (v^8)) Log[(3^(1/4))+v])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))-(((Sqrt[2]) v (45+18 (Sqrt[3]) (v^2)+6 (v^4)+6 (Sqrt[3]) (v^6)+5 (v^8)) Log[(Sqrt[3])+(v^2)])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))+(((Sqrt[2]) v (45+6 (v^4)+5 (v^8)) Log[3+(v^4)])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)));

dFG3vNEW[v_]=((DFG3a (v^3))/(2 (((3+(v^4)))^2)))-(((Sqrt[2]) (v^3) (-162 (Sqrt[3])+81 (v^2)+216 (Sqrt[3]) (v^4)+270 (v^6)+72 (Sqrt[3]) (v^8)-18 (v^10)+18 (v^14)+2 (Sqrt[3]) (v^16)+(v^18)))/((3^(3/4)) (-3+(v^4)) (((3+(v^4)))^4) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((4 (Sqrt[2]) (v^3) (3 (Sqrt[3])+6 (v^2)+(Sqrt[3]) (v^4)) ArcTan[((v^2)/(Sqrt[3]))])/((3^(3/4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((4 (Sqrt[2]) (3^(1/4)) (v^7) (3 (Sqrt[3])+6 (v^2)+(Sqrt[3]) (v^4)) Log[2])/((-3+(v^4)) (((3+(v^4)))^3) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (27-81 (v^4)-48 (Sqrt[3]) (v^6)-27 (v^8)+(v^12)) Log[(3^(1/4))-v])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (27-81 (v^4)-48 (Sqrt[3]) (v^6)-27 (v^8)+(v^12)) Log[(3^(1/4))+v])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (-3+(v^4)) (3+4 (Sqrt[3]) (v^2)+(v^4)) Log[(Sqrt[3])+(v^2)])/((Sqrt[2]) (3^(3/4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((v (9-18 (v^4)+(v^8)) Log[3+(v^4)])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)));

subsSOLFGwDERo012=Union[subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],D[subsSOLFG,v,v,v],D[subsSOLFG,v,v,v,v]];

eqnFG1o0//.subsSOLFGwDERo012//Simplify
eqnFG2o0//.subsSOLFGwDERo012//Simplify
eqnFG3o0//.subsSOLFGwDERo012//Simplify
eqnFG4o0//.subsSOLFGwDERo012//Simplify
eqnFG5o0//.subsSOLFGwDERo012//Simplify

eqnFG1o1//.subsSOLFGwDERo012//Simplify
eqnFG2o1//.subsSOLFGwDERo012//Simplify
eqnFG3o1//.subsSOLFGwDERo012//Simplify
eqnFG4o1//.subsSOLFGwDERo012//Simplify
eqnFG5o1//.subsSOLFGwDERo012//Simplify

eqnFG1o2//.subsSOLFGwDERo012//Simplify
Series[eqnFG2o2//.subsSOLFGwDERo012//Simplify,{v,0,30}]
Series[eqnFG3o2//.subsSOLFGwDERo012//Simplify,{v,0,30}]
eqnFG4o2//.subsSOLFGwDERo012//Simplify
Series[eqnFG5o2//.subsSOLFGwDERo012//Simplify,{v,0,30}]

cFG3[v_]=dFG3[v]-(1/2)bFG3[v];

formFG1o3=Simplify/@(Collect[Expand[eqnFG1o3-(eqnFG1o3//.{aFG3[v]->0,aFG3'[v]->0,aFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0})],{aFG3[v],aFG3'[v],aFG3''[v],bFG3[v],bFG3'[v],bFG3''[v],dFG3[v],dFG3'[v],dFG3''[v]}]//.subsSOLFGwDERo012)

formFG2o3=Simplify/@(Collect[Expand[eqnFG2o3-(eqnFG2o3//.{aFG3[v]->0,aFG3'[v]->0,aFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0})],{aFG3[v],aFG3'[v],aFG3''[v],bFG3[v],bFG3'[v],bFG3''[v],dFG3[v],dFG3'[v],dFG3''[v]}]//.subsSOLFGwDERo012)

formFG3o3=Simplify/@(Collect[Expand[eqnFG3o3-(eqnFG3o3//.{aFG3[v]->0,aFG3'[v]->0,aFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0})],{aFG3[v],aFG3'[v],aFG3''[v],bFG3[v],bFG3'[v],bFG3''[v],dFG3[v],dFG3'[v],dFG3''[v]}]//.subsSOLFGwDERo012)

formFG4o3=Simplify/@(Collect[Expand[eqnFG4o3-(eqnFG4o3//.{aFG3[v]->0,aFG3'[v]->0,aFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0})],{aFG3[v],aFG3'[v],aFG3''[v],bFG3[v],bFG3'[v],bFG3''[v],dFG3[v],dFG3'[v],dFG3''[v]}]//.subsSOLFGwDERo012)

formFG5o3=Simplify/@(Collect[Expand[eqnFG5o3-(eqnFG5o3//.{aFG3[v]->0,aFG3'[v]->0,aFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0})],{aFG3[v],aFG3'[v],aFG3''[v],bFG3[v],bFG3'[v],bFG3''[v],dFG3[v],dFG3'[v],dFG3''[v]}]//.subsSOLFGwDERo012)

Series[Expand[eqnFG1o3//.Union[{aFG3'[v]->aFG3vNEW[v],aFG3''[v]->aFG3vNEW'[v],dFG3'[v]->dFG3vNEW[v],dFG3''[v]->dFG3vNEW'[v]},subsSOLFGwDERo012]],{v,0,30}]

Series[Expand[eqnFG4o3//.Union[{aFG3'[v]->aFG3vNEW[v],aFG3''[v]->aFG3vNEW'[v],dFG3'[v]->dFG3vNEW[v],dFG3''[v]->dFG3vNEW'[v]},subsSOLFGwDERo012]],{v,0,30}]

Series[Expand[eqnFG3o3+2eqnFG5o3//.Union[{aFG3'[v]->aFG3vNEW[v],aFG3''[v]->aFG3vNEW'[v],dFG3'[v]->dFG3vNEW[v],dFG3''[v]->dFG3vNEW'[v]},subsSOLFGwDERo012]],{v,0,15}]

bFG3vNEWS[v_]=Normal[(Simplify/@Series[(bFG3'[v]/.Flatten[Solve[eqnFG2o3==0,bFG3'[v]]//Expand])//.Union[subsSOLFGwDERo012,{dFG3[v]->Integrate[Series[dFG3vNEW[v],{v,0,100}],v],dFG3'[v]->dFG3vNEW[v],dFG3''[v]->dFG3vNEW'[v],aFG3'[v]->aFG3vNEW[v]}]//Expand,{v,0,80}])//.Log[ah_Integer]->xxx[ah]];

COORDINATE TRANSFORMATION

This part contains coordinate transformation from EF solution to FG solution up to the third order in gradients.
  
Section subsCOMBO contains simplifying substitutions.
  
Section EF SOL LOAD must be evaluated to load EF solution.
    
Section FG SOL LOAD must be evaluated to load FG solution.

Section Initialization contains all the machinery to find the coordinate transformation
  
Subsubtitle ORDERS 0-2 contains checks that coordinate transformation works up to the second order

Subsubtitle ORDER 3 contains checks that coordinate transformation works up in the third order

HOW DOES THE COORDINATE TRANSFORMATION WORK?
  
1) The metric in EF coordinates take the form

(ds^2) = 2 dt dr -(r^2) AEF[t, r] (dt^2) + (((1+r t))^2)Exp[bEF[t,r]](dy^2)+(r^2)Exp[cEF[t,r]] (((Subscript[dx, 1])^2)+((Subscript[dx, 2])^2))

There is no (dr^2) term, bot mixing dt dr is present. The metric is invertible for any t and r > 0 providing that b and c does not have any logarithmic singularities.

2) The metric in FG coordinates take the form

(ds^2)= -(1/(z^2))(Exp[aFG[τ,z]]((dτ)^2) + (τ^2)Exp[bFG[τ,z]](dy^2)+Exp[c[τ,z]] (((Subscript[dx, 1])^2)+((Subscript[dx, 2])^2))+(dz^2)) 

There is no mixing term and the radial term is fixed to be (1/(z^2)).

3) Functions AEF, bEF, cEF and aFG, bFG, cFG can be gradient-expanded in t and τ respectivly. E.g.

AEF[t,r]=AEF0[r (t^(1/3))]+(1/(t^(2/3)))AEF1[r (t^(1/3))]+(1/(t^(4/3)))AEF2[r (t^(1/3))]+...
bEF[t,r]=bEF0[r (t^(1/3))]+(1/(t^(2/3)))bEF1[r (t^(1/3))]+(1/(t^(4/3)))bEF2[r (t^(1/3))]+...
cEF[t,r]=cEF0[r (t^(1/3))]+(1/(t^(2/3)))cEF1[r (t^(1/3))]+(1/(t^(4/3)))cEF2[r (t^(1/3))]+...

and

aFG[τ,z]=aFG0[z (τ^(-1/3))]+(1/(τ^(2/3)))aFG1[z (τ^(-1/3))]+(1/(τ^(4/3)))aFG2[z (τ^(-1/3))]+...
bFG[τ,z]=bFG0[z (τ^(-1/3))]+(1/(τ^(2/3)))bFG1[z (τ^(-1/3))]+(1/(τ^(4/3)))bFG2[z (τ^(-1/3))]+...
cFG[τ,z]=cFG0[z (τ^(-1/3))]+(1/(τ^(2/3)))cFG1[z (τ^(-1/3))]+(1/(τ^(4/3)))cFG2[z (τ^(-1/3))]+...

4) By saying that there exists the coordinate transformation from EF to FG coordinates we mean that there two functions of τ and z variables

t[τ,z] and r[τ,z] 

which takes the metric in EF form

(ds^2) = 2 dt[τ,z] dr[τ,z] -((r[τ,z])^2) AEF[t[τ,z], r[τ,z]] ((dt[τ,z])^2) + (((1+r[τ,z] t[τ,z]))^2)Exp[bEF[t[τ,z],r[τ,z]]](dy^2)+((r[τ,z])^2)Exp[cEF[t[τ,z],r[τ,z]]] (((Subscript[dx, 1])^2)+((Subscript[dx, 2])^2))

into the metric in FG form

5) Because warp factors in both cases are expanded in gradients, the coordinate transformation must also be exanded in gradients:

t[τ_,z_]=τ(t0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))t1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))t2[(z/(τ^(1/3)))]+(1/(τ^2))t3[(z/(τ^(1/3)))]+(1/(τ^(8/3)))t4[(z/(τ^(1/3)))])
r[τ_,z_]=(1/z)(r0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))r1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))r2[(z/(τ^(1/3)))]+(1/(τ^2))r3[(z/(τ^(1/3)))]+(1/(τ^(8/3)))r4[(z/(τ^(1/3)))])

6) Functions t0[v], t1[v], t2[v], t3[v]... and r0[v], r1[v], r2[v], r3[v]... can be found order be order solving equations

(ds^2)=(...== 0) dτ dz+(...==(1/(z^2)))(dz^2)+REST.
These are first order differential equations. If the coordinate transformation works, the REST should be the same as the metric in FG coordinates found in [hep-th/0703243].

7) However, this is tough, since equations get more and more complicated at each order. To simplify our task, we use the fact, that we have the explicit expressions for both metric up to the third order. Coordinate transformation is found then order by order:

a) equations

(...== 0) dτ dz
and
(...==(1/(z^2)))(dz^2)
are used to established derivatives of transformation functions at given order

b) Given derivatives, one can find the transformation functions in terms of both EF and FG warp factors comparing transformed parts of the metric at

((Subscript[dx, 1])^2)
and
(dt^2) (or (dy^2))

with the original metric in FG coordinates. This gives two linear equations for two functions, which can be easily solved.

c) There are now 3 cross-checks:

I: transformed part of the metric at (dy^2) (or (dt^2)) must also agree with the original one in FG coordinates
II and III: derivatives of transformation functions obtained in point b) must be equal to the derivative calculated in the point a)

IF THESE CONDITIONS ARE MET UP TO SOME ORDER IN THE GRADIENT EXPANSION, TWO METRICS ARE EQUIVALENT UP TO THIS ORDER.

FOLLOWING CALCULATION SHOWS THAT THIS IS INDEED THE CASE IN ORDER 0, 1, 2 AND 3*. THIS ALSO PROVES THAT LOGARITHMIC SINGULARITY IN THE EXPANSION OF THE SQUARE OF RIEMANN TENSOR IS INDEED A COORDINATE ARTIFACT AS CLAIMED IN THE VER. 1 OF 0805.3774 [HEP-TH].

* In the third order the transformation is shown to work only up to ((O[v])^12), where v is the FG scaling variable. More time spent on evaluation of this notebook should provide more accurate answer. It took around 24 hours to evaluate this notebook on Centrino Duo 2.6 GHz, 4 GB RAM

subsCOMBO

xxx[ch_Integer]:=FactorInteger[ch]/.{List[ah_Integer,bh_Integer]->bh Log[ah],List->Plus}

subsCOMBO={Log[ah_Integer]->xxx[ah],Log[ah_Complex]->Log[Abs[ah]]+I Arg[ah],(E^(2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)+I 2Sin[ah]Cos[ah],(E^(-2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)-I 2Sin[ah]Cos[ah],Log[Times[ah_,bh_]]->Log[ah]+Log[bh],Log[Times[ah_,bh_,ch_]]->Log[ah]+Log[bh]+Log[ch],Log[(1/(ah_))]->-Log[ah],

Log[v-(I/w)]->Log[v w-I]-Log[w],Log[v+(I/w)]->Log[v w+I]-Log[w],Log[v w-I]->Log[1+(v^2)(w^2)]-Log[I+v w],Log[1-((1/2)-(I/2)) (1+v w)]->Log[1+(v^2)(w^2)]-Log[1-((1/2)+(I/2)) (1+v w)]-Log[2],Log[1+I v w]->Log[I]+Log[-I+v w],Log[1-I v w]->Log[-I]+Log[I+v w],Log[1-((1/2)+(I/2)) (v-(I/w)) w]->2Log[-1+v w]-Log[2]-Log[1-((1/2)-(I/2)) (v+(I/w)) w],
Log[((v w)/(Sqrt[1+(v^2) (w^2)]))]->Log[v]+Log[w]-(1/2)Log[1+(v^2)(w^2)],Log[-1+(v^4) (w^4)]->Log[-1+v w]+Log[1+v w]+Log[1+(v^2)(w^2)],Log[1+(1/2) I (v+(I/w)) w]->Log[1+(v^2)(w^2)]-Log[4]-Log[1-(1/2) I (v-(I/w)) w],Log[1-v w]->I π+Log[-1+v w],Log[(1+I)-(1-I) v w]->Log[2]+Log[1+(v^2)(w^2)]-Log[(1-I)-(1+I) v w],ArcTan[((1+v w)/(1-v w))]->ArcTan[((-1+v w)/(1+v w))]-(π/2),ArcTan[((1+v w)/(-1+v w))]->-ArcTan[((-1+v w)/(1+v w))]+(π/2),ArcTan[((1-v w)/(1+v w))]->-ArcTan[((-1+v w)/(1+v w))],
Log[(1-I)-(1+I)v w]->Log[1+I]+Log[I+v w]-I π,Log[((1/2)+(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[-1+v w],Log[((1/2)-(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-1+v w],Log[v-(1/w)]->Log[-1+v w]-Log[w],Log[((1/2)-(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[I+v w],Log[((1/2)+(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[1+v w],Log[((1/2)+(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[I+v w],Log[((1/2)-(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[-I+v w],Log[((1/2)+(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-I+v w],Log[((1/2)-(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[1+v w],Log[1-(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))+(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[v]+Log[w]-Log[I+v w],Log[1-I ((1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2))))]->Log[1+I]+Log[1+v w]-Log[I+v w],Log[1+(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[I]-I π-Log[-I+v w],Log[v+(1/w)]->Log[1+v w]-Log[w],Log[1-(1/2) I (v-(I/w)) w]->-Log[2]+Log[I+v w]-I (π/2),Log[1+((1/2)+(I/2)) (I+v w)]->Log[(1/2)+(I/2)]+Log[1+v w],Log[1-((1/2)+(I/2)) (1+v w)]->Log[(1/2)+(I/2)]+Log[I+v w]-I π,Log[1+(1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+I (π/2)-Log[I+v w],Log[(((1+v w))^2)]->2Log[1+v w], Log[-1+(v^2) (w^2)]->Log[-1+v w]+Log[1+v w]};

Simplify/@Series[Drop[subsCOMBO,7]//.Rule[ah_,bh_]->ah-bh,{v,∞,10}]//.{w->35}//N//Chop

EF SOL LOAD

subsSOLo012={AEF0[v_]->1-(1/((v^4) (w^4))),AEF1[v_]->((2 (1+v w))/(3 (v^5) (w^4)))+((2 D1a (1+(v^4) (w^4)))/(3 (v^5) (w^4))),bEF1[v_]->-(4/(3 v))+((2 D1a)/(3 v))+((π w)/3)-(2/3) w ArcTan[v w]-(4/3) w Log[v]-(4/3) w Log[w]+(2/3) w Log[1+v w]+(1/3) w Log[1+(v^2) (w^2)],cEF1[v_]->(2/(3 v))+((2 D1a)/(3 v))-((π w)/6)+(1/3) w ArcTan[v w]+(2/3) w Log[v]+(2/3) w Log[w]-(1/3) w Log[1+v w]-(1/6) w Log[1+(v^2) (w^2)],AEF2[v_]->(((D1a^2) (-3+(v^4) (w^4)))/(9 (v^6) (w^4)))+((2 D1a (-3-2 v w+3 (v^4) (w^4)))/(9 (v^6) (w^4)))-((2 (D2a+D2a (v^4) (w^4)))/(3 (v^5) (w^4)))+((-2+v w (-4-v w+2 (v^3) (w^3)))/(6 (v^6) (w^4)))+(((1+(v^4) (w^4)) ArcTan[v w])/(3 (v^5) (w^3)))-((Log[2])/(9 (v^4) (w^2)))-((2 Log[v])/(3 (v^4) (w^2)))-((2 Log[w])/(3 (v^4) (w^2)))+((Log[1+(v^2) (w^2)])/(3 (v^4) (w^2))),bEF2'[v_]->bEF2v[v],bEF2v[v_]->((2 (D1a^2))/(9 (v^3)))+((2 D2a)/(3 (v^2)))+((2 π (w^2) (1+v w (1+v w)))/(9 v (1+v w) (1+(v^2) (w^2))))+((4 D1a (1+v w (3+v w (5+v w (7+3 v w (3+v w (2+v w)))))))/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((16+v w (26+v w (43+v w (60+v w (34+11 v w (2+v w))))))/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((w (3+4 v w-7 (v^4) (w^4)) ArcTan[v w])/(9 ((v^2)-(v^6) (w^4))))+(((w^2) Log[16])/(9 v-9 (v^5) (w^4)))+((8 (v^2) (w^5) Log[v])/(9-9 (v^4) (w^4)))+((8 (v^2) (w^5) Log[w])/(9-9 (v^4) (w^4)))+((4 (w^2) (1+v w (1+v w)) Log[1+v w])/(9 v (1+v w) (1+(v^2) (w^2))))+((2 (w^2) (1+v w (-1+v w)) Log[1+(v^2) (w^2)])/(9 v (-1+v w) (1+(v^2) (w^2)))),dEF2[v_]->-(D1a/(3 (v^2)))-((D1a^2)/(6 (v^2)))-(D2a/v)+((π (w^2))/12)-((-4+4 v w)/(12 (v^2)))-((w (-3+v w) ArcTan[v w])/(6 v))-(2/3) (w^2) Log[v]-(2/3) (w^2) Log[w]+(1/6) (w^2) Log[1+v w]+(1/4) (w^2) Log[1+(v^2) (w^2)],cEF2[v_]->-((bEF2[v])/2)+dEF2[v]};

subsSOLo012DER1={AEF0'[v_]->(4/((v^5) (w^4))),AEF1'[v_]->-((2 (5+4 v w))/(3 (v^6) (w^4)))-((2 D1a (5+(v^4) (w^4)))/(3 (v^6) (w^4))),bEF1'[v_]->-((2 D1a)/(3 (v^2)))+(4/(3 (v^2) (1+v w) (1+(v^2) (w^2)))),cEF1'[v_]->-((2 D1a)/(3 (v^2)))-(2/(3 (v^2) (1+v w) (1+(v^2) (w^2)))),AEF2'[v_]->((6+10 v w+(v^2) (w^2)-(v^4) (w^4))/(3 (v^7) (w^4)))-((2 (D1a^2) (-9+(v^4) (w^4)))/(9 (v^7) (w^4)))+((2 D2a (5+(v^4) (w^4)))/(3 (v^6) (w^4)))-((4 D1a (-9-5 v w+3 (v^4) (w^4)))/(9 (v^7) (w^4)))-(((5+(v^4) (w^4)) ArcTan[v w])/(3 (v^6) (w^3)))+((4 Log[2])/(9 (v^5) (w^2)))+((8 Log[v])/(3 (v^5) (w^2)))+((8 Log[w])/(3 (v^5) (w^2)))-((4 Log[1+(v^2) (w^2)])/(3 (v^5) (w^2))),bEF2''[v_]->bEF2v'[v],bEF2v'[v_]->-((2 (D1a^2))/(3 (v^4)))-((4 D2a)/(3 (v^3)))-((2 π (w^2) (1+v w (2+v w (3+2 v w (3+v w (2+v w))))))/(9 (v^2) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((4 D1a (3+v w (11+3 v w (1+v w) (8+v w (6+v w (12+v w (8+3 v w (4+v w (2+v w)))))))))/(9 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((2 (-24+v w (-42+v w (-62+v w (-82+v w (-33+v w (-8+v w (47+v w (102+v w (37+11 v w (2+v w)))))))))))/(9 (v^4) (-1+v w) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((2 w (3+v w (8+v w (13+v w (18+7 v w (3+v w (2+v w)))))) ArcTan[v w])/(9 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((4 (w^2) (-1+5 (v^4) (w^4)) Log[2])/(9 (v^2) (((-1+(v^4) (w^4)))^2)))+((16 v (w^5) (1+(v^4) (w^4)) Log[v])/(9 (((-1+(v^4) (w^4)))^2)))+((16 v ((w^5)+(v^4) (w^9)) Log[w])/(9 (((-1+(v^4) (w^4)))^2)))-((4 (w^2) (1+v w (2+v w (3+2 v w (3+v w (2+v w))))) Log[1+v w])/(9 (v^2) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((2 (w^2) (1+v w (-2+v w (3-2 v w (3+v w (-2+v w))))) Log[1+(v^2) (w^2)])/(9 (v^2) (((-1+v w))^2) (((1+(v^2) (w^2)))^2))),dEF2'[v_]->((2 D1a)/(3 (v^3)))+((D1a^2)/(3 (v^3)))+(D2a/(v^2))-((4+v w (2+3 v w (1+v w)))/(6 (v^3) (1+v w) (1+(v^2) (w^2))))-((w ArcTan[v w])/(2 (v^2))),cEF2'[v_]->-(1/2) bEF2'[v]+dEF2'[v]};

subsSOLo012DER2={AEF0''[v_]->-(20/((v^6) (w^4))),AEF1''[v_]->((4 D1a ((v^4)+(15/(w^4))))/(3 (v^7)))+((20 (3+2 v w))/(3 (v^7) (w^4))),bEF1''[v_]->((4 D1a)/(3 (v^3)))-((4 (2+v w (3+v w (4+5 v w))))/(3 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2))),cEF1''[v_]->((4 D1a)/(3 (v^3)))+((4+2 v w (3+v w (4+5 v w)))/(3 (v^3) (((1+v w))^2) (((1+(v^2) (w^2)))^2))),AEF2''[v_]->((2 (D1a^2) (-21+(v^4) (w^4)))/(3 (v^8) (w^4)))-((4 D2a (15+(v^4) (w^4)))/(3 (v^7) (w^4)))+((4 D1a (-21-10 v w+3 (v^4) (w^4)))/(3 (v^8) (w^4)))+((-42+2 v w (-30+v w (-22+v w (-30-v w+(v^3) (w^3)))))/(3 (v^8) (w^4) (1+(v^2) (w^2))))+((2 (15+(v^4) (w^4)) ArcTan[v w])/(3 (v^7) (w^3)))-((20 Log[2])/(9 (v^6) (w^2)))-((40 Log[v])/(3 (v^6) (w^2)))-((40 Log[w])/(3 (v^6) (w^2)))+((20 Log[1+(v^2) (w^2)])/(3 (v^6) (w^2))),Derivative[3][bEF2][v_]->bEF2v''[v],bEF2v''[v_]->((8 (D1a^2))/(3 (v^5)))+((4 D2a)/(v^4))+((4 π (w^2) (1+3 v w (1+v w (2+v w (1+v w) (3+v w (1+v w (4+v w (2+v w))))))))/(9 (v^3) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((8 D1a (2+v w (9+v w (24+v w (50+v w (82+v w (110+v w (124+v w (114+v w (102+v w (85+6 v w (10+v w (4+v w)))))))))))))/(3 (v^5) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-(2 (96+v w (174+v w (253+v w (332+v w (26+v w (-218+v w (-421+v w (-624+v w (-456+v w (-326+v w (119+3 v w (188+v w (42+11 v w (2+v w)))))))))))))))/(9 (v^5) (((-1+v w))^2) (((1+v w))^4) (((1+(v^2) (w^2)))^4))-((2 w (9+v w (31+3 v w (22+v w (38+v w (48+v w (52+v w (50+7 v w (6+v w (3+v w))))))))) ArcTan[v w])/(9 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((8 (w^2) (1+15 (v^8) (w^8)) Log[2])/(9 (v^3) (((-1+(v^4) (w^4)))^3)))-((16 (w^5) (1+12 (v^4) (w^4)+3 (v^8) (w^8)) Log[v])/(9 (((-1+(v^4) (w^4)))^3)))-((16 (w^5) (1+12 (v^4) (w^4)+3 (v^8) (w^8)) Log[w])/(9 (((-1+(v^4) (w^4)))^3)))+((8 (w^2) (1+3 v w (1+v w (2+v w (1+v w) (3+v w (1+v w (4+v w (2+v w))))))) Log[1+v w])/(9 (v^3) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 (w^2) (1+3 v w (-1+v w (2+v w (-1+v w) (3+v w (-1+v w (4+v w (-2+v w))))))) Log[1+(v^2) (w^2)])/(9 (v^3) (((-1+v w))^3) (((1+(v^2) (w^2)))^3))),dEF2''[v_]->-((2 D1a)/(v^4))-((D1a^2)/(v^4))-((2 D2a)/(v^3))+((6+v w (10+v w (13+v w (2+v w) (8+3 (v^2) (w^2)))))/(3 (v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((w ArcTan[v w])/(v^3)),cEF2''[v_]->-(1/2) bEF2''[v]+dEF2''[v]};

subsSOLo012DER3={Derivative[3][AEF0][v_]->(120/((v^7) (w^4))),Derivative[3][AEF1][v_]->-((20 (7+4 v w))/((v^8) (w^4)))-((4 D1a (35+(v^4) (w^4)))/((v^8) (w^4))),Derivative[3][bEF1][v_]->-((4 D1a)/(v^4))+((8 (3+v w (8+3 v w (5+v w (8+v w (9+v w (8+5 v w)))))))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3))),Derivative[3][cEF1][v_]->-((4 D1a)/(v^4))-((4 (3+8 v w+15 (v^2) (w^2)+24 (v^3) (w^3)+27 (v^4) (w^4)+24 (v^5) (w^5)+15 (v^6) (w^6)))/(3 (v^4) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^3))),Derivative[3][AEF2][v_]->((4 D2a ((v^4)+(35/(w^4))))/(v^8))+((2 (D1a^2) (-4 (v^4)+(168/(w^4))))/(3 (v^9)))+((8 D1a (84+35 v w-6 (v^4) (w^4)))/(3 (v^9) (w^4)))+((336+2 v w (210+v w (337+v w (420+v w (175+v w (210+5 v w-3 (v^3) (w^3)))))))/(3 (v^9) (w^4) (((1+(v^2) (w^2)))^2)))-((2 (35+(v^4) (w^4)) ArcTan[v w])/((v^8) (w^3)))+((40 Log[2])/(3 (v^7) (w^2)))+((80 Log[v])/((v^7) (w^2)))+((80 Log[w])/((v^7) (w^2)))-((40 Log[1+(v^2) (w^2)])/((v^7) (w^2))),Derivative[4][bEF2][v_]->Derivative[3][bEF2v][v],Derivative[3][bEF2v][v_]->-((40 (D1a^2))/(3 (v^6)))-((16 D2a)/(v^5))-((4 π (w^2) (1+v w (4+v w (10+v w (20+v w (30+v w (36+v w (34+v w (40+v w (45+4 v w (10+v w (4+v w))))))))))))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-(1/(3 (v^6) (((1+v w))^5) (((1+(v^2) (w^2)))^5)))16 D1a (5+v w (27+v w (85+v w (205+v w (395+v w (635+v w (877+v w (1045+v w (1055+v w (905+v w (675+v w (527+5 v w (77+3 v w (15+v w (5+v w)))))))))))))))+(1/(9 (v^6) (((-1+v w))^3) (((1+v w))^5) (((1+(v^2) (w^2)))^5)))4 (-240+v w (-444+v w (-645+v w (-846+v w (153+v w (964+v w (1787+v w (2610+v w (735+v w (-760+v w (-1133+3 v w (-502+v w (-827+v w (-732+v w (-25+11 v w (62+v w (9+2 v w (2+v w))))))))))))))))))+(1/(3 (v^5) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))8 w (3+v w (13+v w (34+v w (70+v w (113+v w (150+7 v w (24+v w (22+v w (19+v w (15+v w (10+v w (4+v w)))))))))))) ArcTan[v w]+((8 (w^2) (-1+5 (v^4) (w^4) (1+5 (v^4) (w^4)+7 (v^8) (w^8))) Log[2])/(3 (v^4) (((-1+(v^4) (w^4)))^4)))+((64 (v^3) (w^9) (5+10 (v^4) (w^4)+(v^8) (w^8)) Log[v])/(3 (((-1+(v^4) (w^4)))^4)))+((64 (v^3) (w^9) (5+10 (v^4) (w^4)+(v^8) (w^8)) Log[w])/(3 (((-1+(v^4) (w^4)))^4)))-((8 (w^2) (1+v w (4+v w (10+v w (20+v w (30+v w (36+v w (34+v w (40+v w (45+4 v w (10+v w (4+v w))))))))))) Log[1+v w])/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))-(1/(3 (v^4) (((-1+v w))^4) (((1+(v^2) (w^2)))^4)))4 (w^2) (-1+v w (4+v w (-10+v w (20+v w (-30+v w (36+v w (-34+v w (40+v w (-45+4 v w (10+v w (-4+v w))))))))))) Log[1+(v^2) (w^2)],Derivative[3][dEF2][v_]->((8 D1a)/(v^5))+((4 (D1a^2))/(v^5))+((6 D2a)/(v^4))-((24+v w (66+v w (121+v w (189+v w (201+v w (173+3 v w (41+v w (17+3 v w (3+v w)))))))))/(3 (v^5) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((3 w ArcTan[v w])/(v^4)),Derivative[3][cEF2][v_]->-(1/2) Derivative[3][bEF2][v]+Derivative[3][dEF2][v]};

subsSOLo012DER4={Derivative[4][AEF0][v_]->-(840/((v^8) (w^4))),Derivative[4][AEF1][v_]->D1a ((16/(v^5))+(1120/((v^9) (w^4))))+(1120/((v^9) (w^4)))+(560/((v^8) (w^3))),Derivative[4][bEF1][v_]->-(32/(v^5))+((16 D1a)/(v^5))+((32 w)/(v^4))-((16 (w^2))/((v^3) (1+v w)))-((16 w (1+2 v w+3 (v^2) (w^2)))/((v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))-((16 (w^3))/((v^2)+(v^4) (w^2)))+((16 (w^2))/((v^3)+(v^5) (w^2)))-((16 w (1+3 v w+6 (v^2) (w^2)+18 (v^3) (w^3)+21 (v^4) (w^4)+15 (v^5) (w^5)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))-((8 w (1+4 v w+10 (v^2) (w^2)+16 (v^3) (w^3)+30 (v^4) (w^4)+60 (v^5) (w^5)+114 (v^6) (w^6)+96 (v^7) (w^7)+45 (v^8) (w^8)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4))),Derivative[4][cEF1][v_]->(16/(v^5))+((16 D1a)/(v^5))-((16 w)/(v^4))+((8 (w^2))/((v^3) (1+v w)))+((8 w (1+2 v w+3 (v^2) (w^2)))/((v^4) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+((8 (w^3))/((v^2)+(v^4) (w^2)))-((8 (w^2))/((v^3)+(v^5) (w^2)))+((8 w (1+3 v w+6 (v^2) (w^2)+18 (v^3) (w^3)+21 (v^4) (w^4)+15 (v^5) (w^5)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 w (1+4 v w+10 (v^2) (w^2)+16 (v^3) (w^3)+30 (v^4) (w^4)+60 (v^5) (w^5)+114 (v^6) (w^6)+96 (v^7) (w^7)+45 (v^8) (w^8)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4))),Derivative[4][AEF2][v_]->(40/(v^6))-(1008/((v^10) (w^4)))-(1120/((v^9) (w^3)))+(856/(3 (v^8) (w^2)))-((32 (w^6))/(((1+(v^2) (w^2)))^4))-((160 (w^4))/(3 (v^2) (((1+(v^2) (w^2)))^3)))-((100 (w^2))/((v^4) (((1+(v^2) (w^2)))^2)))-((80 (w^4))/(((v+(v^3) (w^2)))^2))-((400 (w^2))/((v^4)+(v^6) (w^2)))-(240/((v^6)+(v^8) (w^2)))-((16 (w^4) (1+(v^4) (w^4)))/((v^2) (((1+(v^2) (w^2)))^4)))-((56 (w^2) (1+(v^4) (w^4)))/((v^4) (((1+(v^2) (w^2)))^3)))-((152 (1+(v^4) (w^4)))/((v^6) (((1+(v^2) (w^2)))^2)))-((448 (1+(v^4) (w^4)))/((v^8) (w^2) (1+(v^2) (w^2))))-((16 D2a (70+(v^4) (w^4)))/((v^9) (w^4)))+((8 (D1a^2) (-378+5 (v^4) (w^4)))/(3 (v^10) (w^4)))+((136 (1+5 (v^4) (w^4)))/(3 (v^6) (((1+(v^2) (w^2)))^2)))+((16 D1a (-378-140 v w+15 (v^4) (w^4)))/(3 (v^10) (w^4)))+((168+840 (v^4) (w^4))/((v^8) (w^2)+(v^10) (w^4)))+((32 w (w+5 (v^4) (w^5)))/(3 (v^4) (((1+(v^2) (w^2)))^3)))+((8 (70+(v^4) (w^4)) ArcTan[v w])/((v^9) (w^3)))-((280 Log[2])/(3 (v^8) (w^2)))-((560 Log[v])/((v^8) (w^2)))-((560 Log[w])/((v^8) (w^2)))+((280 Log[1+(v^2) (w^2)])/((v^8) (w^2))),Derivative[5][bEF2][v_]->Derivative[4][bEF2v][v],Derivative[4][bEF2v][v_]->((80 (D1a^2))/(v^7))+((80 D2a)/(v^6))+(1/(3 (v^5) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))16 π (w^2) (1+5 v w+15 (v^2) (w^2)+35 (v^3) (w^3)+65 (v^4) (w^4)+101 (v^5) (w^5)+135 (v^6) (w^6)+140 (v^7) (w^7)+115 (v^8) (w^8)+85 (v^9) (w^9)+101 (v^10) (w^10)+105 (v^11) (w^11)+75 (v^12) (w^12)+25 (v^13) (w^13)+5 (v^14) (w^14))+(1/(3 (v^7) (((1+v w))^6) (((1+(v^2) (w^2)))^6)))160 D1a (3+19 v w+69 (v^2) (w^2)+189 (v^3) (w^3)+416 (v^4) (w^4)+768 (v^5) (w^5)+1224 (v^6) (w^6)+1704 (v^7) (w^7)+2100 (v^8) (w^8)+2301 (v^9) (w^9)+2218 (v^10) (w^10)+1809 (v^11) (w^11)+1260 (v^12) (w^12)+810 (v^13) (w^13)+576 (v^14) (w^14)+378 (v^15) (w^15)+189 (v^16) (w^16)+54 (v^17) (w^17)+9 (v^18) (w^18))-(1/(9 (v^7) (((-1+v w))^4) (((1+v w))^6) (((1+(v^2) (w^2)))^6)))8 (720+1350 v w+1965 (v^2) (w^2)+2580 (v^3) (w^3)-1122 (v^4) (w^4)-4274 (v^5) (w^5)-7345 (v^6) (w^6)-10416 (v^7) (w^7)-2994 (v^8) (w^8)+2868 (v^9) (w^9)+11004 (v^10) (w^10)+19140 (v^11) (w^11)+1518 (v^12) (w^12)-8704 (v^13) (w^13)-2516 (v^14) (w^14)+3672 (v^15) (w^15)-13614 (v^16) (w^16)-13842 (v^17) (w^17)-2505 (v^18) (w^18)+8832 (v^19) (w^19)+900 (v^20) (w^20)+330 (v^21) (w^21)+165 (v^22) (w^22))-(1/(3 (v^6) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))8 w (15+79 v w+245 (v^2) (w^2)+585 (v^3) (w^3)+1115 (v^4) (w^4)+1775 (v^5) (w^5)+2429 (v^6) (w^6)+2865 (v^7) (w^7)+2885 (v^8) (w^8)+2485 (v^9) (w^9)+1855 (v^10) (w^10)+1379 (v^11) (w^11)+945 (v^12) (w^12)+525 (v^13) (w^13)+175 (v^14) (w^14)+35 (v^15) (w^15)) ArcTan[v w]-((32 ((w^2)-5 (v^4) (w^6)+45 (v^8) (w^10)+145 (v^12) (w^14)+70 (v^16) (w^18)) Log[2])/(3 (v^5) (((-1+(v^4) (w^4)))^5)))-((64 (v^2) (w^9) (15+135 (v^4) (w^4)+101 (v^8) (w^8)+5 (v^12) (w^12)) Log[v])/(3 (((-1+(v^4) (w^4)))^5)))-((64 (v^2) (w^9) (15+135 (v^4) (w^4)+101 (v^8) (w^8)+5 (v^12) (w^12)) Log[w])/(3 (((-1+(v^4) (w^4)))^5)))+(1/(3 (v^5) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^5)))32 (w^2) (1+5 v w+15 (v^2) (w^2)+35 (v^3) (w^3)+65 (v^4) (w^4)+101 (v^5) (w^5)+135 (v^6) (w^6)+140 (v^7) (w^7)+115 (v^8) (w^8)+85 (v^9) (w^9)+101 (v^10) (w^10)+105 (v^11) (w^11)+75 (v^12) (w^12)+25 (v^13) (w^13)+5 (v^14) (w^14)) Log[1+v w]+(1/(3 (v^5) (((-1+v w))^5) (((1+(v^2) (w^2)))^5)))16 (w^2) (1-5 v w+15 (v^2) (w^2)-35 (v^3) (w^3)+65 (v^4) (w^4)-101 (v^5) (w^5)+135 (v^6) (w^6)-140 (v^7) (w^7)+115 (v^8) (w^8)-85 (v^9) (w^9)+101 (v^10) (w^10)-105 (v^11) (w^11)+75 (v^12) (w^12)-25 (v^13) (w^13)+5 (v^14) (w^14)) Log[1+(v^2) (w^2)],Derivative[4][dEF2][v_]->(40/(v^6))-((40 D1a)/(v^6))-((20 (D1a^2))/(v^6))-((24 D2a)/(v^5))-((8 w)/(v^5))-((8 (w^2))/(v^4))-((6 (w^4))/((v^2) (((1+v w))^2)))+((8 (w^3))/((v^3) (1+v w)))-((36 (w^6))/(((1+(v^2) (w^2)))^2))+((12 (w^4) (-3+v w))/(((v+(v^3) (w^2)))^2))+((42 (w^4))/((v^2)+(v^4) (w^2)))-((12 (w^3))/((v^3)+(v^5) (w^2)))+((4 (w^2) (-3+v w))/((v^4)+(v^6) (w^2)))+((32 (w^2) (1+3 v w+6 (v^2) (w^2)+5 (v^3) (w^3)+3 (v^4) (w^4)))/(3 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((4 (w^2) (1+4 v w+10 (v^2) (w^2)+30 (v^3) (w^3)+53 (v^4) (w^4)+68 (v^5) (w^5)+44 (v^6) (w^6)+18 (v^7) (w^7)))/(3 (v^4) (((1+v w))^4) (((1+(v^2) (w^2)))^4)))+((12 w ArcTan[v w])/(v^5)),Derivative[4][cEF2][v_]->-(1/2) Derivative[4][bEF2][v]+Derivative[4][dEF2][v]};

subsSOLbEF2={bEF2[v_]->(8/(9 (v^2)))-((2 D1a)/(9 (v^2)))-((D1a^2)/(9 (v^2)))-((2 D2a)/(3 v))-((2 w)/(3 v))-((4 D1a w)/(9 v))+((Catalan (w^2))/9)+((π (w^2))/9)+((7/216)-((11 I)/432)) (π^2) (w^2)-((2 (w^2))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))-((2 v (w^3))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((2 (v^2) (w^4))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((4 D1a (v^2) (w^4))/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((w ArcTan[v w])/(3 v))-(2/9) (w^2) ArcTan[v w]+((1/9)+(I/18)) π (w^2) ArcTan[v w]-((1/9)-(I/9)) (w^2) ((ArcTan[v w])^2)-(5/36) π (w^2) Log[2]+(1/18) (w^2) ((Log[2])^2)-(10/9) (w^2) Log[v]+(4/9) (w^2) Log[2] Log[v]-(10/9) (w^2) Log[w]+((5/18)-((2 I)/9)) π (w^2) Log[w]-(2/3) (w^2) ArcTan[v w] Log[w]+(4/9) (w^2) ArcTan[((-1+v w)/(1+v w))] Log[w]+((4/9)-(I/9)) (w^2) Log[2] Log[w]-(2/9) (w^2) Log[v] Log[1-v w]-(1/9) I (w^2) Log[w] (-Log[2]+Log[1-I v w])-(1/9) (w^2) Log[2] Log[-1+v w]-(2/9) (w^2) Log[w] Log[-1+v w]+(1/9) π (w^2) (-((I π)/2)+Log[2]-Log[-I+v w])-(4/9) (w^2) ArcTan[v w] (Log[2]+Log[v]+Log[w]-Log[I+v w])+(1/9) I (w^2) Log[2] Log[I+v w]-(4/9) I (w^2) Log[v] Log[I+v w]-(1/9) I (w^2) Log[w] Log[I+v w]-(1/9) (w^2) (-Log[2]+Log[1-I v w]) Log[I+v w]-(2/9) (w^2) Log[-1+v w] Log[I+v w]+(2/9) (w^2) (Log[-(1/2)+(I/2)]+Log[-1+v w]) Log[I+v w]+(1/18) (w^2) ((Log[I+v w])^2)+(2/9) (w^2) Log[1+v w]-(1/9) π (w^2) Log[1+v w]+(1/9) I (w^2) Log[2] Log[1+v w]+(2/9) (w^2) Log[v] Log[1+v w]+(2/9) (w^2) Log[w] Log[1+v w]+(2/9) I (w^2) (Log[-(1/2)-(I/2)]+Log[I+v w]) Log[1+v w]-(1/9) (w^2) ((Log[1+v w])^2)+(1/18) π (w^2) (Log[1+I]-Log[I+v w]+Log[1+v w])+(2/9) (w^2) ArcTan[v w] (Log[1+I]-Log[I+v w]+Log[1+v w])+(4/9) (w^2) Log[1+(v^2) (w^2)]-(2/9) (w^2) Log[2] Log[1+(v^2) (w^2)]+(2/9) I (w^2) Log[v] Log[1+(v^2) (w^2)]+(1/9) I (w^2) Log[w] Log[1+(v^2) (w^2)]+((1/18)+(I/18)) (w^2) (-Log[2]+Log[1-I v w]) Log[1+(v^2) (w^2)]+(2/9) (w^2) Log[-1+v w] Log[1+(v^2) (w^2)]-(1/9) (w^2) (Log[-(1/2)+(I/2)]+Log[-1+v w]) Log[1+(v^2) (w^2)]-((1/9)+(I/9)) (w^2) Log[1+v w] Log[1+(v^2) (w^2)]+((1/36)-(I/36)) (w^2) ((Log[1+(v^2) (w^2)])^2)-(1/18) π (w^2) Log[Sin[(π/4)+ArcTan[v w]]]-(2/9) (w^2) PolyLog[2,-v w]+((2/9)+((2 I)/9)) (w^2) PolyLog[2,-I v w]+((2/9)-((2 I)/9)) (w^2) PolyLog[2,I v w]-(2/9) (w^2) PolyLog[2,v w]+((1/18)-(I/18)) (w^2) PolyLog[2,(1/2)-((I v w)/2)]+((1/18)+(I/18)) (w^2) PolyLog[2,(1/2)+((I v w)/2)]+(1/9) (w^2) PolyLog[2,((1/2)+(I/2)) (-I+v w)]+(2/9) I (w^2) PolyLog[2,((I-v w)/(I+v w))]-(1/9) I (w^2) PolyLog[2,-((1+I v w)/(I+v w))]+(1/9) (w^2) PolyLog[2,((1/2)-(I/2)) (I+v w)]-((1/9)+(I/9)) (w^2) PolyLog[2,((1/2)-(I/2)) (1+v w)]-((1/9)-(I/9)) (w^2) PolyLog[2,((1/2)+(I/2)) (1+v w)]};

subsSOLo012wDERupto4=Union[subsSOLo012,subsSOLo012DER1,subsSOLo012DER2,subsSOLo012DER3,subsSOLo012DER4];

AEF3NEW[v_]=(1/(v^4))(-(((7/81)-((13 I)/72))/w)+((2 I Catalan)/(9 w))-((((59/432)-(I/9)) π)/w)+((((11/216)-(I/36)) (π^2))/w)+((((2/81)-(I/72)) Log[2])/w)+((((25/54)+(I/9)) π Log[2])/w)+((((17/324)-(I/18)) ((Log[2])^2))/w)-((2 Log[w])/(9 w))-((((1/18)+(I/6)) π Log[w])/w)+((((1/3)-(I/9)) Log[2] Log[w])/w)+((((4/9)+((4 I)/9)) ((Log[w])^2))/w)+((((1/81)+((2 I)/81)) PolyLog[2,(1/2)-(I/2)])/w)+((((1/81)-((2 I)/81)) PolyLog[2,(1/2)+(I/2)])/w)+((((17/162)+((7 I)/81)) PolyLog[2,1-I])/w)-((((19/162)-((11 I)/81)) PolyLog[2,1+I])/w))-(1/(27 (v^3)))-((2 D3a)/(3 v))+(4/(27 (v^7) (w^4)))+((4 (D1a^3))/(27 (v^7) (w^4)))-((2 D3a)/(3 (v^5) (w^4)))+(4/(9 (v^6) (w^3)))+(1/(9 (v^5) (w^2)))-((13 I)/(72 (v^4) w))-(w/(54 (v^2)))+((2 (D1a^2) (2+v w))/(9 (v^7) (w^4)))-((2 D1a D2a (-3+(v^4) (w^4)))/(9 (v^6) (w^4)))-((2 D2a (-3-2 v w+5 (v^4) (w^4)))/(9 (v^6) (w^4)))+((π (40+51 v w+32 (v^3) (w^3)+40 (v^4) (w^4)))/(432 (v^5) (w^2)))-(((18+2 I ((6+I)+3 π) (v^2) (w^2)-22 (v^4) (w^4)+3 (-3+2 π) (v^5) (w^5)+3 v (w+2 π w)) ArcTan[v w])/(54 (v^6) (w^3)))+(((1+2 I v w+(v^4) (w^4)) ((ArcTan[v w])^2))/(9 (v^5) (w^2)))-(((1+(v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))])/(27 (v^5) (w^2)))+(((32+3 I v w) Log[2])/(216 (v^5) (w^2)))+((π (1-8 v w+(v^4) (w^4)) Log[2])/(36 (v^5) (w^2)))-((4 ArcTan[v w] Log[2])/(9 (v^4) w))-(((1+(v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))] Log[2])/(9 (v^5) (w^2)))+((((1/9)+(I/9)) π (1-2 I v w+(v^4) (w^4)) Log[v])/((v^5) (w^2)))-((2 (-6+3 v w+4 (v^3) (w^3)+6 (v^4) (w^4)) Log[v])/(27 (v^5) (w^2)))-((2 ArcTan[v w] Log[v])/(9 (v^4) w))+((4 Log[2] Log[v])/(9 (v^4) w))+((I π ((4+I)-(1+5 I) v w+(4+I) (v^4) (w^4)) Log[w])/(18 (v^5) (w^2)))-((2 ArcTan[v w] Log[w])/(9 (v^4) w))+((2 (1+(v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))] Log[w])/(9 (v^5) (w^2)))+((2 (4-4 (v^3) (w^3)-8 (v^4) (w^4)+3 (1+(v^4) (w^4)) ArcTanh[v w]) Log[w])/(27 (v^5) (w^2)))+((((1/9)+(I/9)) Log[2] Log[w])/((v^4) w))-((((4/9)+((4 I)/9)) ((Log[w])^2))/((v^4) w))+(((1-v w+(v^4) (w^4)) Log[2] Log[-1+v w])/(18 (v^5) (w^2)))+(((1-2 v w+(v^4) (w^4)) Log[v] Log[-1+v w])/(9 (v^5) (w^2)))+((2 (1-v w+(v^4) (w^4)) Log[w] Log[-1+v w])/(9 (v^5) (w^2)))-((((2/9)-(I/9)) Log[I+v w])/((v^4) w))-((I π (1-(3-I) v w+(v^4) (w^4)) Log[I+v w])/(18 (v^5) (w^2)))+((4 ArcTan[v w] Log[I+v w])/(9 (v^4) w))-((Log[2] Log[I+v w])/(9 (v^4) w))+((2 I (1+(v^4) (w^4)) Log[v] Log[I+v w])/(9 (v^5) (w^2)))-((π (1+I v w+(v^4) (w^4)) Log[1+v w])/(6 (v^5) (w^2)))+((4 (1+v w+(v^3) (w^3)+(v^4) (w^4)) Log[1+v w])/(27 (v^5) (w^2)))-(((1-(1+2 I) v w+(v^4) (w^4)) Log[2] Log[1+v w])/(18 (v^5) (w^2)))-(((1+2 v w+(v^4) (w^4)) Log[v] Log[1+v w])/(9 (v^5) (w^2)))-((2 (1+v w+(v^4) (w^4)) Log[w] Log[1+v w])/(9 (v^5) (w^2)))+((2 (-I+v w-I (v^4) (w^4)) Log[I+v w] Log[1+v w])/(9 (v^5) (w^2)))+((I π (1-(2-5 I) v w+(v^4) (w^4)) Log[1+(v^2) (w^2)])/(36 (v^5) (w^2)))+(((-16+(8-3 I) v w+4 (v^3) (w^3)+8 (v^4) (w^4)) Log[1+(v^2) (w^2)])/(54 (v^5) (w^2)))-((((1/6)-(I/18)) Log[2] Log[1+(v^2) (w^2)])/((v^4) w))+(((-I+2 v w-I (v^4) (w^4)) Log[v] Log[1+(v^2) (w^2)])/(9 (v^5) (w^2)))+((2 Log[w] Log[1+(v^2) (w^2)])/(9 (v^4) w))-(((1-v w+(v^4) (w^4)) Log[-1+v w] Log[1+(v^2) (w^2)])/(18 (v^5) (w^2)))+((((1+2 I)-(3+2 I) v w+(1+2 I) (v^4) (w^4)) Log[1+v w] Log[1+(v^2) (w^2)])/(18 (v^5) (w^2)))+((D1a (12+18 v w+3 (v^4) (w^4)+3 v w (-3+(v^4) (w^4)) ArcTan[v w]+(v^2) (w^2) Log[4]+12 (v^2) (w^2) Log[v]+12 (v^2) (w^2) Log[w]-6 (v^2) (w^2) Log[1+(v^2) (w^2)]))/(27 (v^7) (w^4)))-(((1+6 v w+(v^4) (w^4)) PolyLog[2,-v w])/(9 (v^5) (w^2)))-((I (1+(1+3 I) v w+(v^4) (w^4)) PolyLog[2,-I v w])/(9 (v^5) (w^2)))+(((I+(3+I) v w+I (v^4) (w^4)) PolyLog[2,I v w])/(9 (v^5) (w^2)))+(((1-2 v w+(v^4) (w^4)) PolyLog[2,v w])/(9 (v^5) (w^2)))+((PolyLog[2,-(v^2) (w^2)])/(18 (v^4) w))+((((1/18)+(I/9)) PolyLog[2,(1/2) ((1+I)-(1-I) v w)])/((v^4) w))-((PolyLog[2,(-(1/2)-(I/2)) (-1+v w)])/(18 (v^4) w))-((PolyLog[2,(-(1/2)+(I/2)) (-1+v w)])/(18 (v^4) w))+(((1-4 I v w+(v^4) (w^4)) PolyLog[2,(-(1/2)+(I/2)) (-I+v w)])/(18 (v^5) (w^2)))+((PolyLog[2,((1/2)+(I/2)) (-I+v w)])/(18 (v^4) w))-(((1+(v^4) (w^4)) PolyLog[2,((1/2)+(I/2)) (-I+v w)])/(18 (v^5) (w^2)))+((I PolyLog[2,((I-v w)/(I+v w))])/(9 (v^4) w))+((I PolyLog[2,((-I+v w)/(I+v w))])/(9 (v^4) w))+((((5/18)-(I/3)) PolyLog[2,(-(1/2)-(I/2)) (I+v w)])/((v^4) w))+(((1+4 I v w+(v^4) (w^4)) PolyLog[2,(-(1/2)-(I/2)) (I+v w)])/(18 (v^5) (w^2)))+((PolyLog[2,((1/2)-(I/2)) (I+v w)])/(18 (v^4) w))-(((1+(v^4) (w^4)) PolyLog[2,((1/2)-(I/2)) (I+v w)])/(18 (v^5) (w^2)))-((5 PolyLog[2,((1/2)-(I/2)) (1+v w)])/(18 (v^4) w))+((I (1-v w+(v^4) (w^4)) PolyLog[2,((1/2)-(I/2)) (1+v w)])/(9 (v^5) (w^2)))-((((1/18)+((2 I)/9)) PolyLog[2,((1/2)+(I/2)) (1+v w)])/((v^4) w))-((I (1-v w+(v^4) (w^4)) PolyLog[2,((1/2)+(I/2)) (1+v w)])/(9 (v^5) (w^2)));

bEF3vNEW[v_]=-((2 (D1a^3))/(27 (v^4)))-((4 D1a D2a)/(9 (v^3)))+((6 D3a)/(v^2))+((8 D3a)/(3 (v^6) (w^4)))+((4 D3a)/(3 (v^5) (w^3)))+((16 D3a (v^2) (w^4))/(3-3 (v^4) (w^4)))+(((π^2) (w^3) ((-76+106 I)+(14-29 I) (v^3) (w^3)))/(324 v (-1+(v^4) (w^4))))+((4 D3a w)/(3 v-3 (v^5) (w^4)))-((8 D3a)/(3 (v^2)-3 (v^6) (w^4)))+((8 Catalan (w^3)-4 Catalan (v^3) (w^6))/(27 v-27 (v^5) (w^4)))-((4 D2a (1+3 v w+5 (v^2) (w^2)+7 (v^3) (w^3)+9 (v^4) (w^4)+6 (v^5) (w^5)+3 (v^6) (w^6)))/(9 (v^3) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))-((4 D3a)/(3 (v^5) (w^3)-3 (v^9) (w^7)))-((8 D3a)/(3 (v^6) (w^4)-3 (v^10) (w^8)))-((2 (D1a^2) (3+11 v w+24 (v^2) (w^2)+42 (v^3) (w^3)+54 (v^4) (w^4)+60 (v^5) (w^5)+60 (v^6) (w^6)+54 (v^7) (w^7)+27 (v^8) (w^8)+9 (v^9) (w^9)))/(27 (v^4) (((1+v w))^3) (((1+(v^2) (w^2)))^3)))+((π (8+16 v w+16 (v^2) (w^2)+25 (v^3) (w^3)+85 (v^4) (w^4)+77 (v^5) (w^5)+91 (v^6) (w^6)+77 (v^7) (w^7)+(v^8) (w^8)+(v^9) (w^9)+3 (v^10) (w^10)))/(54 (v^5) w (-1+v w) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))-(1/(27 (v^5) w (-1+v w) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^3)))2 D1a (v w (-3-12 v w-19 (v^2) (w^2)-26 (v^3) (w^3)-21 (v^4) (w^4)+8 (v^5) (w^5)+7 (v^6) (w^6)+6 (v^7) (w^7)+44 (v^8) (w^8)+32 (v^9) (w^9)+16 (v^10) (w^10))+π (-2-4 v w-6 (v^2) (w^2)-9 (v^3) (w^3)-10 (v^4) (w^4)-11 (v^5) (w^5)-14 (v^6) (w^6)-11 (v^7) (w^7)-6 (v^8) (w^8)-(v^9) (w^9)+4 (v^10) (w^10)+4 (v^11) (w^11)+2 (v^12) (w^12)))-(208+v w (384+v w (564+v w ((642+117 I)+v w ((88+234 I)+v w ((-252+351 I)+v w ((-656+468 I)+v w ((-952+351 I)+v w ((-432+234 I)+v w ((-156+117 I)+2 v w (-6+31 v w)))))))))))/(108 (v^4) (-1+v w) (((1+v w))^3) (((1+(v^2) (w^2)))^3))+((2 D1a (-4-4 v w-7 (v^2) (w^2)-9 (v^3) (w^3)-9 (v^4) (w^4)-9 (v^5) (w^5)-7 (v^6) (w^6)+3 (v^7) (w^7)+7 (v^8) (w^8)+7 (v^9) (w^9)) ArcTan[v w])/(27 (v^5) w (-1+v w) (((1+v w))^2) (((1+(v^2) (w^2)))^2)))+(1/(54 (v^5) w (-1+v w) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))(-16-32 v w-44 (v^2) (w^2)-(55+6 π) (v^3) (w^3)-2 ((65+36 I)+(7+26 I) π) (v^4) (w^4)-(4+2 I) ((30+3 I)+(8+9 I) π) (v^5) (w^5)-2 ((71+36 I)+(7+26 I) π) (v^6) (w^6)+2 ((-46-36 I)+(3-22 I) π) (v^7) (w^7)+(15+(14+8 I) π) (v^8) (w^8)+(15+(14+8 I) π) (v^9) (w^9)+(-25+(14+8 I) π) (v^10) (w^10)) ArcTan[v w]+(((w^2) (-3 I+(7-4 I) v w+(4+7 I) (v^2) (w^2)-(7-4 I) (v^3) (w^3)) ((ArcTan[v w])^2))/(27 (v^2) (-I+v w) (-1+(v^2) (w^2))))+(((w^2) (-2+87 v w+2 (v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))])/(54 (v^2) (-1+(v^4) (w^4))))-((π (w^2) (-3+260 v w+3 (v^4) (w^4)) Log[2])/(108 (v^2) (-1+(v^4) (w^4))))+((4 D1a (w^2) (-1+5 (v^4) (w^4)) Log[2])/(27 (v^2) (((-1+(v^4) (w^4)))^2)))+((I (w^2) (24 I-(9+128 I) v w+(9+128 I) (v^2) (w^2)-(9+128 I) (v^3) (w^3)+(9+56 I) (v^4) (w^4)) Log[2])/(108 (v^2) (1+v w) (((-1+v w-(v^2) (w^2)+(v^3) (w^3)))^2)))-((4 (w^3) (-1+3 (v^3) (w^3)) ArcTan[v w] Log[2])/(27 v (-1+(v^4) (w^4))))+(((w^2) (-1-4 v w+(v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))] Log[2])/(9 (v^2) (-1+(v^4) (w^4))))+((2 (w^3) (-2+(v^3) (w^3)) ((Log[2])^2))/(27 v (-1+(v^4) (w^4))))-((((1/27)+(I/27)) π (w^2) (-3+(2+6 I) v w+(7+4 I) (v^4) (w^4)) Log[v])/((v^2) (-1+(v^4) (w^4))))-((4 v (w^5) (-7-5 v w-6 (v^2) (w^2)-(v^4) (w^4)+7 (v^5) (w^5)) Log[v])/(27 (((-1+(v^4) (w^4)))^2)))+((16 D1a (v (w^5)+(v^5) (w^9)) Log[v])/(27 (((-1+(v^4) (w^4)))^2)))-((4 (w^3) (-9+4 (v^3) (w^3)) ArcTan[v w] Log[v])/(27 v (-1+(v^4) (w^4))))+((16 (v^2) (w^6) Log[2] Log[v])/(27 (-1+(v^4) (w^4))))+((π (w^2) ((-3+12 I)+(30+38 I) v w+(19-28 I) (v^4) (w^4)) Log[w])/(54 (v^2) (-1+(v^4) (w^4))))+((16 D1a (v (w^5)+(v^5) (w^9)) Log[w])/(27 (((-1+(v^4) (w^4)))^2)))-((4 (w^3) (-3+10 (v^3) (w^3)) ArcTan[v w] Log[w])/(27 v (-1+(v^4) (w^4))))+((2 (w^2) (3+20 v w+5 (v^4) (w^4)) ArcTan[((-1+v w)/(1+v w))] Log[w])/(27 (v^2) (-1+(v^4) (w^4))))-((2 (w^2) (2 (-1+9 v w-7 (v^3) (w^3)-3 (v^4) (w^4)-15 (v^5) (w^5)-(v^7) (w^7)+6 (v^8) (w^8))+3 (((-1+(v^4) (w^4)))^2) ArcTanh[v w]) Log[w])/(27 (v^2) (((-1+(v^4) (w^4)))^2)))+((((-54+18 I) (w^3) Log[2]+16 (v^3) (w^6) Log[2]) Log[w])/(27 v (-1+(v^4) (w^4))))+(((8+8 I) (w^3) ((Log[w])^2))/(3 v-3 (v^5) (w^4)))-(((w^2) (-3-10 v w+11 (v^4) (w^4)) Log[2] Log[-1+v w])/(54 (v^2) (-1+(v^4) (w^4))))-(((w^2) (-3+11 v w-11 (v^2) (w^2)+11 (v^3) (w^3)) Log[v] Log[-1+v w])/(27 (v^2) (-1+v w) (1+(v^2) (w^2))))-((2 (w^2) (-3+7 v w-7 (v^2) (w^2)+7 (v^3) (w^3)) Log[w] Log[-1+v w])/(27 (v^2) (-1+v w) (1+(v^2) (w^2))))+((8 I D1a (1+(v^4) (w^4)) Log[I+v w])/(27 (v^5) w (-1+(v^4) (w^4))))+((π (w^2) (-3 I+(10-14 I) v w+(4+19 I) (v^4) (w^4)) Log[I+v w])/(54 (v^2) (-1+(v^4) (w^4))))+((2 I (4+4 v w+(9+18 I) (v^4) (w^4)) Log[I+v w])/(27 (v^5) w (-1+(v^4) (w^4))))+((8 (w^3) (1-v w+(v^2) (w^2)) ArcTan[v w] Log[I+v w])/(27 v (-1+v w) (1+(v^2) (w^2))))+((2 I (w^3) ((2+9 I)+2 (v^3) (w^3)) Log[2] Log[I+v w])/(27 v (-1+(v^4) (w^4))))-((2 I (w^2) (-3-4 v w+11 (v^4) (w^4)) Log[v] Log[I+v w])/(27 (v^2) (-1+(v^4) (w^4))))-((8 I (w^3) (1-v w+(v^2) (w^2)) Log[w] Log[I+v w])/(27 v (-1+v w) (1+(v^2) (w^2))))-((2 (w^3) (-2+(v^3) (w^3)) ((Log[I+v w])^2))/(27 v (-1+(v^4) (w^4))))+((π (w^2) (-9-(24+54 I) v w+17 (v^4) (w^4)) Log[1+v w])/(54 (v^2) (-1+(v^4) (w^4))))-((4 D1a (w^2) (1+2 v w+3 (v^2) (w^2)+6 (v^3) (w^3)+4 (v^4) (w^4)+2 (v^5) (w^5)) Log[1+v w])/(27 (v^2) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((2 (w^2) (-4+4 (v^2) (w^2)+(v^3) (w^3)+4 (v^4) (w^4)+3 (v^5) (w^5)+2 (v^6) (w^6)) Log[1+v w])/(27 (v^2) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((8 (w^3) (1+v w+(v^2) (w^2)) ArcTan[v w] Log[1+v w])/(27 v (1+v w) (1+(v^2) (w^2))))+(((w^2) (-3-(2-36 I) v w+3 (v^4) (w^4)) Log[2] Log[1+v w])/(54 (v^2) (-1+(v^4) (w^4))))+(((w^2) (3+11 v w+11 (v^2) (w^2)+11 (v^3) (w^3)) Log[v] Log[1+v w])/(27 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((2 (w^2) (3+7 v w+7 (v^2) (w^2)+7 (v^3) (w^3)) Log[w] Log[1+v w])/(27 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((2 I (w^2) (-3-(8+18 I) v w+7 (v^4) (w^4)) Log[I+v w] Log[1+v w])/(27 (v^2) (-1+(v^4) (w^4))))-((4 (w^3) (1+v w+(v^2) (w^2)) ((Log[1+v w])^2))/(27 v (1+v w) (1+(v^2) (w^2))))-((π (w^2) (-3 I+(6-32 I) v w+(12+19 I) (v^4) (w^4)) Log[1+(v^2) (w^2)])/(108 (v^2) (-1+(v^4) (w^4))))-(2 D1a (-2 I+2 I v w-2 I (v^2) (w^2)-(1-2 I) (v^3) (w^3)+(1-2 I) (v^4) (w^4)-(1-2 I) (v^5) (w^5)+(3-2 I) (v^6) (w^6)+(2+2 I) (v^7) (w^7)-2 (v^8) (w^8)+2 (v^9) (w^9)) Log[1+(v^2) (w^2)])/(27 (v^5) w (((-1+v w))^2) (1+v w) (((1+(v^2) (w^2)))^2))+(((4 I+4 I v w+4 (v^3) (w^3)-(26-5 I) (v^4) (w^4)-4 I (v^5) (w^5)-7 (v^6) (w^6)-16 (v^7) (w^7)+(10-9 I) (v^8) (w^8)-(v^10) (w^10)+12 (v^11) (w^11)) Log[1+(v^2) (w^2)])/(27 (v^5) w (((-1+(v^4) (w^4)))^2)))-((((5/27)-(I/9)) (w^3) ((-1-2 I)+(1+I) (v^3) (w^3)) Log[2] Log[1+(v^2) (w^2)])/(v (-1+(v^4) (w^4))))+((I (w^2) (-3-(4+8 I) v w+11 (v^4) (w^4)) Log[v] Log[1+(v^2) (w^2)])/(27 (v^2) (-1+(v^4) (w^4))))+((4 (w^3) ((2+I)+I (v^3) (w^3)) Log[w] Log[1+(v^2) (w^2)])/(27 v (-1+(v^4) (w^4))))+(((w^2) (-3-10 v w+11 (v^4) (w^4)) Log[-1+v w] Log[1+(v^2) (w^2)])/(54 (v^2) (-1+(v^4) (w^4))))+((2 (w^3) ((-2+I)+(1+I) (v^3) (w^3)) Log[I+v w] Log[1+(v^2) (w^2)])/(27 v (-1+(v^4) (w^4))))-(((w^2) ((-3-6 I)+(26+20 I) v w+(11+14 I) (v^4) (w^4)) Log[1+v w] Log[1+(v^2) (w^2)])/(54 (v^2) (-1+(v^4) (w^4))))+((((1/27)-(I/27)) (w^3) (-1-I v w+(v^2) (w^2)) ((Log[1+(v^2) (w^2)])^2))/(v (-I+v w) (-1+(v^2) (w^2))))-((2 π (w^3) (-2+(v^3) (w^3)) Log[Sin[(π/4)+ArcTan[v w]]])/(27 v (-1+(v^4) (w^4))))-(1/(v-(v^5) (w^4)))6 (w^4) (-(((7/81)-((13 I)/72))/w)+((2 I Catalan)/(9 w))-((((59/432)-(I/9)) π)/w)+((((11/216)-(I/36)) (π^2))/w)+((((2/81)-(I/72)) Log[2])/w)+((((25/54)+(I/9)) π Log[2])/w)+((((17/324)-(I/18)) ((Log[2])^2))/w)-((2 Log[w])/(9 w))-((((1/18)+(I/6)) π Log[w])/w)+((((1/3)-(I/9)) Log[2] Log[w])/w)+((((4/9)+((4 I)/9)) ((Log[w])^2))/w)+((((1/81)+((2 I)/81)) PolyLog[2,(1/2)-(I/2)])/w)+((((1/81)-((2 I)/81)) PolyLog[2,(1/2)+(I/2)])/w)+((((17/162)+((7 I)/81)) PolyLog[2,1-I])/w)-((((19/162)-((11 I)/81)) PolyLog[2,1+I])/w))-(((w^2) (3+5 v w-5 (v^2) (w^2)+5 (v^3) (w^3)) PolyLog[2,-v w])/(27 (v^2) (-1+v w) (1+(v^2) (w^2))))+(((w^2) (-3 I-(10+22 I) v w+(8+11 I) (v^4) (w^4)) PolyLog[2,-I v w])/(27 (v^2) (-1+(v^4) (w^4))))-((I (w^2) (-3-(22+10 I) v w+(11+8 I) (v^4) (w^4)) PolyLog[2,I v w])/(27 (v^2) (-1+(v^4) (w^4))))-(((w^2) (-3+11 v w-11 (v^2) (w^2)+11 (v^3) (w^3)) PolyLog[2,v w])/(27 (v^2) (-1+v w) (1+(v^2) (w^2))))-(((w^3) PolyLog[2,-(v^2) (w^2)])/(3 v-3 (v^5) (w^4)))-(((2-(4+4 I) v w-5 (v^4) (w^4)+(4+4 I) (v^5) (w^5)+7 (v^8) (w^8)) PolyLog[2,(1/2) ((1+I)-(1-I) v w)])/(18 (v^6) (w^2) (-1+(v^4) (w^4))))-((2 I (w^3) ((1-2 I)+(1+I) (v^3) (w^3)) PolyLog[2,(1/2)-((I v w)/2)])/(27 v (-1+(v^4) (w^4))))+((2 (w^3) ((-2+I)+(1+I) (v^3) (w^3)) PolyLog[2,(1/2)+((I v w)/2)])/(27 v (-1+(v^4) (w^4))))+(((w^3) PolyLog[2,(-(1/2)-(I/2)) (-1+v w)])/(3 v-3 (v^5) (w^4)))+(((w^3) PolyLog[2,(-(1/2)+(I/2)) (-1+v w)])/(3 v-3 (v^5) (w^4)))+(((1-(2+2 I) v w-2 (v^4) (w^4)-(1+4 I) (v^5) (w^5)+3 (v^8) (w^8)) PolyLog[2,(-(1/2)+(I/2)) (-I+v w)])/(9 (v^6) (w^2) (-1+(v^4) (w^4))))+(((w^2) (-3-10 v w+11 (v^4) (w^4)) PolyLog[2,((1/2)+(I/2)) (-I+v w)])/(54 (v^2) (-1+(v^4) (w^4))))+((2 I (w^3) (-11+4 (v^3) (w^3)) PolyLog[2,((I-v w)/(I+v w))])/(27 v (-1+(v^4) (w^4))))-((4 I (w^3) (-2+(v^3) (w^3)) PolyLog[2,-((1+I v w)/(I+v w))])/(27 v (-1+(v^4) (w^4))))+((2 I (w^3) PolyLog[2,((-I+v w)/(I+v w))])/(3 v (-1+(v^4) (w^4))))-(((w^2) (-1-(18-12 I) v w+(v^4) (w^4)) PolyLog[2,(-(1/2)-(I/2)) (I+v w)])/(18 (v^2) (-1+(v^4) (w^4))))+(((w^2) (-3-10 v w+11 (v^4) (w^4)) PolyLog[2,((1/2)-(I/2)) (I+v w)])/(54 (v^2) (-1+(v^4) (w^4))))-(((w^2) (-3 I+(13+10 I) v w+(4+7 I) (v^4) (w^4)) PolyLog[2,((1/2)-(I/2)) (1+v w)])/(27 (v^2) (-1+(v^4) (w^4))))+((I (w^2) (-3-(26+23 I) v w+(7+4 I) (v^4) (w^4)) PolyLog[2,((1/2)+(I/2)) (1+v w)])/(27 (v^2) (-1+(v^4) (w^4))));

dEF3NEW[v_]=-(8/(27 (v^3)))+((D1a^2)/(9 (v^3)))+((D1a^3)/(27 (v^3)))+(D2a/(3 (v^2)))+((D1a D2a)/(3 (v^2)))-(D3a/v)+(w/(9 (v^2)))-((w^2)/(9 v))+((Catalan (w^3))/18)-((37/288)+((421 I)/576)) π (w^3)+((13/432)-((5 I)/96)) (π^2) (w^3)+((π (80 (w^2)+(29+421 I) v (w^3)))/(576 v))-((w^3)/(36 (1+v w+(v^2) (w^2)+(v^3) (w^3))))-((v (w^4))/(12 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((w (-24+12 (3-2 π) v w+(37+(8+8 I) π) (v^2) (w^2)) ArcTan[v w])/(144 (v^2)))+(((w^2) (3-(1-3 I) v w) ((ArcTan[v w])^2))/(18 v))-((D1a (-2-4 v w-3 (v^2) (w^2)-3 (v^3) (w^3)+3 v w (1+v w+(v^2) (w^2)+(v^3) (w^3)) ArcTan[v w]))/(18 (v^3) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+(((w^2) (8+29 v w) ArcTan[((1-v w)/(1+v w))])/(144 v))+(((w^2) Log[2])/(9 v))+((17/72)+(I/72)) π (w^3) Log[2]-((π (w^2) (-3+(8+I) v w) Log[2])/(72 v))-(7/18) (w^3) ArcTan[v w] Log[2]+(((w^2) (-3+v w) ArcTan[((-1+v w)/(1+v w))] Log[2])/(18 v))+(1/36) (w^3) ((Log[2])^2)-(2/3) (w^3) Log[v]+((((1/6)+(I/6)) π (w^2) (1-I v w) Log[v])/v)-(4/9) (w^3) ArcTan[v w] Log[v]+(4/9) (w^3) Log[2] Log[v]-(5/12) (w^3) Log[w]-((5/12)+(I/18)) π (w^3) Log[w]+((π (w^2) ((-3+12 I)+(22-4 I) v w) Log[w])/(36 v))-(4/9) (w^3) ArcTan[v w] Log[w]+(((w^2) (-3+v w) ArcTan[((1-v w)/(1+v w))] Log[w])/(9 v))-(((w^2) (8+9 v w-12 ArcTanh[v w]) Log[w])/(36 v))+(4/9) (w^3) Log[2] Log[w]-(((w^2) (-1+v w) Log[2] Log[-1+v w])/(12 v))-(((w^2) (-1+v w) Log[v] Log[-1+v w])/(6 v))-(((w^2) (-2+v w) Log[w] Log[-1+v w])/(6 v))+((π (w^2) (-3 I+(1+7 I) v w) Log[I+v w])/(36 v))+(1/3) (w^3) ArcTan[v w] Log[I+v w]-((I (w^2) (-3+v w) Log[v] Log[I+v w])/(9 v))-(1/36) (w^3) ((Log[I+v w])^2)+((π (w^2) (-9+2 v w) Log[1+v w])/(36 v))+(((w^2) (4+3 v w) Log[1+v w])/(18 v))+(1/9) (w^3) ArcTan[v w] Log[1+v w]+(((w^2) (-3+v w) Log[2] Log[1+v w])/(36 v))-(((w^2) (3+v w) Log[v] Log[1+v w])/(18 v))-(((w^2) (6+v w) Log[w] Log[1+v w])/(18 v))+((I (w^2) (-3+v w) Log[I+v w] Log[1+v w])/(9 v))-(1/18) (w^3) ((Log[1+v w])^2)+(1/8) (w^3) Log[1+(v^2) (w^2)]-(1/12) π (w^3) Log[1+(v^2) (w^2)]-((π (w^2) (-3 I+(2+7 I) v w) Log[1+(v^2) (w^2)])/(72 v))+(((w^2) (-8+9 v w) Log[1+(v^2) (w^2)])/(72 v))-(2/9) (w^3) Log[2] Log[1+(v^2) (w^2)]+(((w^2) (-3 I+(2+I) v w) Log[v] Log[1+(v^2) (w^2)])/(18 v))+(1/9) (w^3) Log[w] Log[1+(v^2) (w^2)]+(((w^2) (-1+v w) Log[-1+v w] Log[1+(v^2) (w^2)])/(12 v))+(1/36) (w^3) Log[I+v w] Log[1+(v^2) (w^2)]-(((w^2) ((-3-6 I)+(3+2 I) v w) Log[1+v w] Log[1+(v^2) (w^2)])/(36 v))+(1/72) (w^3) ((Log[1+(v^2) (w^2)])^2)-(1/36) π (w^3) Log[Sin[(π/4)+ArcTan[v w]]]-(((w^2) (1+3 v w) PolyLog[2,-v w])/(6 v))+(((w^2) (-3 I+(6+I) v w) PolyLog[2,-I v w])/(18 v))-((I (w^2) (-3+(1+6 I) v w) PolyLog[2,I v w])/(18 v))-(((w^2) (-1+v w) PolyLog[2,v w])/(6 v))+((1/12)+(I/6)) (w^3) PolyLog[2,(1/2) ((1+I)-(1-I) v w)]+(1/36) (w^3) PolyLog[2,(1/2)-((I v w)/2)]+(1/36) (w^3) PolyLog[2,(1/2)+((I v w)/2)]+(((w^2) (1-2 I v w) PolyLog[2,(-(1/2)+(I/2)) (-I+v w)])/(12 v))-(((w^2) PolyLog[2,((1/2)+(I/2)) (-I+v w)])/(12 v))+(1/12) (w^3) PolyLog[2,((1/2)+(I/2)) (-I+v w)]+(2/9) I (w^3) PolyLog[2,((I-v w)/(I+v w))]-(1/18) I (w^3) PolyLog[2,-((1+I v w)/(I+v w))]+((1/12)-(I/6)) (w^3) PolyLog[2,(-(1/2)-(I/2)) (I+v w)]+(((w^2) (1+2 I v w) PolyLog[2,(-(1/2)-(I/2)) (I+v w)])/(12 v))-(((w^2) PolyLog[2,((1/2)-(I/2)) (I+v w)])/(12 v))+(1/12) (w^3) PolyLog[2,((1/2)-(I/2)) (I+v w)]-((1/6)-(I/36)) (w^3) PolyLog[2,((1/2)-(I/2)) (1+v w)]-((I (w^2) (-2+v w) PolyLog[2,((1/2)-(I/2)) (1+v w)])/(12 v))-((1/6)+(I/36)) (w^3) PolyLog[2,((1/2)+(I/2)) (1+v w)]+((I (w^2) (-2+v w) PolyLog[2,((1/2)+(I/2)) (1+v w)])/(12 v));

dEF3vNEW[v_]=-((D1a^2)/(3 (v^4)))-((D1a^3)/(9 (v^4)))-((2 D2a)/(3 (v^3)))-((2 D1a D2a)/(3 (v^3)))+(D3a/(v^2))-((w^3)/(18 (v+(v^3) (w^2))))+(8/(9 (v^4) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((14 w)/(9 (v^3) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((41 (w^2))/(18 (v^2) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((97 (w^3))/(36 v (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((4 (w^4))/(3 (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+((7 v (w^5))/(9 (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+(((v^2) (w^6))/(6 (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))-(((v^3) (w^7))/(4 (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))-((w^2)/(9 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))-((w^4)/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))-((π (w^2) (5+3 v w+3 (v^2) (w^2)+(v^3) (w^3)))/(36 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((w (12+(-1+6 π) (v^2) (w^2)+(-1+6 π) (v^3) (w^3)+(-17+6 π) (v^4) (w^4)+3 v (w+2 π w)) ArcTan[v w])/(36 (v^3) (1+v w+(v^2) (w^2)+(v^3) (w^3))))-(((w^2) ((ArcTan[v w])^2))/(6 (v^2)))+((D1a (-3-8 v w-14 (v^2) (w^2)-20 (v^3) (w^3)-19 (v^4) (w^4)-12 (v^5) (w^5)-6 (v^6) (w^6)+3 v w (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2) ArcTan[v w]))/(9 (v^4) (((1+v w+(v^2) (w^2)+(v^3) (w^3)))^2)))+(((w^2) ArcTan[((-1+v w)/(1+v w))])/(18 (v^2)))-((π (w^2) Log[2])/(24 (v^2)))-(((w^2) Log[2])/(9 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+(((w^2) ArcTan[((-1+v w)/(1+v w))] Log[2])/(6 (v^2)))-((((1/6)+(I/6)) π (w^2) Log[v])/(v^2))-((2 v (w^5) Log[v])/(9 (1+v w+(v^2) (w^2)+(v^3) (w^3))))+((((1/12)-(I/3)) π (w^2) Log[w])/(v^2))+(((w^2) ArcTan[((1-v w)/(1+v w))] Log[w])/(3 (v^2)))-(((w^2) (-2 (1+v w+(v^2) (w^2))+3 (1+v w+(v^2) (w^2)+(v^3) (w^3)) ArcTanh[v w]) Log[w])/(9 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))-(((w^2) Log[2] Log[-1+v w])/(12 (v^2)))-(((w^2) Log[v] Log[-1+v w])/(6 (v^2)))-(((w^2) Log[w] Log[-1+v w])/(3 (v^2)))+((I π (w^2) Log[I+v w])/(12 (v^2)))-((I (w^2) Log[v] Log[I+v w])/(3 (v^2)))+((π (w^2) Log[1+v w])/(4 (v^2)))-(((w^2) (2+v w+(v^2) (w^2)) Log[1+v w])/(9 (v^2) (1+v w+(v^2) (w^2)+(v^3) (w^3))))+(((w^2) Log[2] Log[1+v w])/(12 (v^2)))+(((w^2) Log[v] Log[1+v w])/(6 (v^2)))+(((w^2) Log[w] Log[1+v w])/(3 (v^2)))+((I (w^2) Log[I+v w] Log[1+v w])/(3 (v^2)))-((I π (w^2) Log[1+(v^2) (w^2)])/(24 (v^2)))+(((w^2) (2-v w+2 (v^2) (w^2)) Log[1+(v^2) (w^2)])/(18 (v^2) (1+(v^2) (w^2))))+((I (w^2) Log[v] Log[1+(v^2) (w^2)])/(6 (v^2)))+(((w^2) Log[-1+v w] Log[1+(v^2) (w^2)])/(12 (v^2)))-((((1/12)+(I/6)) (w^2) Log[1+v w] Log[1+(v^2) (w^2)])/(v^2))+(((w^2) PolyLog[2,-v w])/(6 (v^2)))+((I (w^2) PolyLog[2,-I v w])/(6 (v^2)))-((I (w^2) PolyLog[2,I v w])/(6 (v^2)))-(((w^2) PolyLog[2,v w])/(6 (v^2)))-(((w^2) PolyLog[2,(1/2) ((1+I)-(1-I) v w)])/(12 (v^2)))+(((w^2) PolyLog[2,((1/2)+(I/2)) (-I+v w)])/(12 (v^2)))-(((w^2) PolyLog[2,(-(1/2)-(I/2)) (I+v w)])/(12 (v^2)))+(((w^2) PolyLog[2,((1/2)-(I/2)) (I+v w)])/(12 (v^2)))-((I (w^2) PolyLog[2,((1/2)-(I/2)) (1+v w)])/(6 (v^2)))+((I (w^2) PolyLog[2,((1/2)+(I/2)) (1+v w)])/(6 (v^2)));

FG SOL LOAD

subsSOLFG={
aFG0[v]->2Log[(3^(1/4))+v]+2Log[(3^(1/4))-v]+2Log[(3^(1/2))+(v^2)]-Log[3+(v^4)]-Log[3],
bFG0[v]->Log[3+(v^4)]-Log[3],
cFG0[v]->Log[3+(v^4)]-Log[3],

aFG1[v]->(((Sqrt[2]) (v^4) (9+(v^4)))/((3^(3/4)) (9-(v^8)))),
bFG1[v]->-(((Sqrt[2]) (v^4))/((3^(3/4)) (3+(v^4))))+(((Sqrt[2]) Log[(3^(1/4))-v])/(3^(3/4)))+(((Sqrt[2]) Log[(3^(1/4))+v])/(3^(3/4)))+(((Sqrt[2]) Log[(Sqrt[3])+(v^2)])/(3^(3/4)))-(((Sqrt[2]) Log[3+(v^4)])/(3^(3/4))),
cFG1[v]->-(((Sqrt[2]) (v^4))/((3^(3/4)) (3+(v^4))))-((Log[(3^(1/4))-v])/((Sqrt[2]) (3^(3/4))))-((Log[(3^(1/4))+v])/((Sqrt[2]) (3^(3/4))))-((Log[(Sqrt[3])+(v^2)])/((Sqrt[2]) (3^(3/4))))+((Log[3+(v^4)])/((Sqrt[2]) (3^(3/4)))),

aFG2[v]->-(((v^2) (-486+243 (Sqrt[3]) (v^2)-270 (v^4)+63 (Sqrt[3]) (v^6)+54 (v^8)+45 (Sqrt[3]) (v^10)+30 (v^12)+(Sqrt[3]) (v^14)))/(36 (((-9+(v^8)))^2)))+(((v^4) (9+(v^4)) Log[2])/(6 (Sqrt[3]) (-9+(v^8))))-((Log[(Sqrt[3])+(v^2)])/(2 (Sqrt[3])))+((Log[3+(v^4)])/(4 (Sqrt[3]))),

bFG2[v]->((π^2)/(72 (Sqrt[3])))-(((v^2) (-162+171 (Sqrt[3]) (v^2)-144 (v^4)+36 (Sqrt[3]) (v^6)-30 (v^8)+(Sqrt[3]) (v^10)))/(36 (-3+(v^4)) (((3+(v^4)))^2)))-((ArcTanh[((v^2)/(Sqrt[3]))])/(2 (Sqrt[3])))+(((v^4) Log[2])/((Sqrt[3]) (18+6 (v^4))))+((Log[(3^(1/4))-v])/(12 (Sqrt[3])))-(((Log[(3^(1/4))-v])^2)/(6 (Sqrt[3])))+((Log[(3^(1/4))+v])/(12 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[(3^(1/4))+v])/(3 (Sqrt[3])))-(((Log[(3^(1/4))+v])^2)/(6 (Sqrt[3])))+((13 Log[(Sqrt[3])+(v^2)])/(12 (Sqrt[3])))-((2 Log[2] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))-((Log[(3^(1/4))+v] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))+(((Log[(Sqrt[3])+(v^2)])^2)/(2 (Sqrt[3])))-((7 Log[3+(v^4)])/(12 (Sqrt[3])))+((Log[2] Log[3+(v^4)])/(3 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[3+(v^4)])/(3 (Sqrt[3])))+((Log[(3^(1/4))+v] Log[3+(v^4)])/(3 (Sqrt[3])))-((Log[(Sqrt[3])+(v^2)] Log[3+(v^4)])/(3 (Sqrt[3])))+((PolyLog[2,-((((-3+(Sqrt[3]) (v^2)))^2)/(((3+(Sqrt[3]) (v^2)))^2))])/(6 (Sqrt[3]))),

cFG2[v]->-((π^2)/(144 (Sqrt[3])))-(((v^2) (162-45 (Sqrt[3]) (v^2)+72 (v^4)-36 (Sqrt[3]) (v^6)+6 (v^8)+(Sqrt[3]) (v^10)))/(36 (-3+(v^4)) (((3+(v^4)))^2)))+(((v^4) Log[2])/((Sqrt[3]) (18+6 (v^4))))+((Log[(3^(1/4))-v])/(12 (Sqrt[3])))+(((Log[(3^(1/4))-v])^2)/(12 (Sqrt[3])))+((Log[(3^(1/4))+v])/(12 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[(3^(1/4))+v])/(6 (Sqrt[3])))+(((Log[(3^(1/4))+v])^2)/(12 (Sqrt[3])))-((5 Log[(Sqrt[3])+(v^2)])/(12 (Sqrt[3])))+((Log[2] Log[(Sqrt[3])+(v^2)])/(3 (Sqrt[3])))+((Log[(3^(1/4))-v] Log[(Sqrt[3])+(v^2)])/(6 (Sqrt[3])))+((Log[(3^(1/4))+v] Log[(Sqrt[3])+(v^2)])/(6 (Sqrt[3])))-(((Log[(Sqrt[3])+(v^2)])^2)/(4 (Sqrt[3])))+((Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[2] Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[(3^(1/4))-v] Log[3+(v^4)])/(6 (Sqrt[3])))-((Log[(3^(1/4))+v] Log[3+(v^4)])/(6 (Sqrt[3])))+((Log[(Sqrt[3])+(v^2)] Log[3+(v^4)])/(6 (Sqrt[3])))-((PolyLog[2,-((((-3+(Sqrt[3]) (v^2)))^2)/(((3+(Sqrt[3]) (v^2)))^2))])/(12 (Sqrt[3])))
};

aFG3vNEW[v_]=-((DFG3a (v^3) (9+2 (v^4)+(v^8)))/(((-9+(v^8)))^2))+(1/(3 (3^(3/4)) (((-9+(v^8)))^4)))2 (Sqrt[2]) (v^3) (4374 (Sqrt[3])-9477 (v^2)+1458 (Sqrt[3]) (v^4)-3402 (v^6)+1944 (Sqrt[3]) (v^8)-1053 (v^10)+432 (Sqrt[3]) (v^12)+108 (v^14)+594 (Sqrt[3]) (v^16)+225 (v^18)+30 (Sqrt[3]) (v^20)+30 (v^22)+(v^26))+((8 (Sqrt[2]) (v^3) (9+2 (v^4)+(v^8)) ArcTan[((v^2)/(Sqrt[3]))])/((3^(1/4)) (((-9+(v^8)))^2)))-((8 (Sqrt[2]) (v^7) (9+18 (v^4)+(v^8)) Log[2])/((3^(1/4)) (((-9+(v^8)))^3)))+(((Sqrt[2]) v (-45+18 (Sqrt[3]) (v^2)-6 (v^4)+6 (Sqrt[3]) (v^6)-5 (v^8)) Log[(3^(1/4))-v])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))+(((Sqrt[2]) v (-45+18 (Sqrt[3]) (v^2)-6 (v^4)+6 (Sqrt[3]) (v^6)-5 (v^8)) Log[(3^(1/4))+v])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))-(((Sqrt[2]) v (45+18 (Sqrt[3]) (v^2)+6 (v^4)+6 (Sqrt[3]) (v^6)+5 (v^8)) Log[(Sqrt[3])+(v^2)])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)))+(((Sqrt[2]) v (45+6 (v^4)+5 (v^8)) Log[3+(v^4)])/(3 (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)));

dFG3vNEW[v_]=((DFG3a (v^3))/(2 (((3+(v^4)))^2)))-(((Sqrt[2]) (v^3) (-162 (Sqrt[3])+81 (v^2)+216 (Sqrt[3]) (v^4)+270 (v^6)+72 (Sqrt[3]) (v^8)-18 (v^10)+18 (v^14)+2 (Sqrt[3]) (v^16)+(v^18)))/((3^(3/4)) (-3+(v^4)) (((3+(v^4)))^4) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((4 (Sqrt[2]) (v^3) (3 (Sqrt[3])+6 (v^2)+(Sqrt[3]) (v^4)) ArcTan[((v^2)/(Sqrt[3]))])/((3^(3/4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((4 (Sqrt[2]) (3^(1/4)) (v^7) (3 (Sqrt[3])+6 (v^2)+(Sqrt[3]) (v^4)) Log[2])/((-3+(v^4)) (((3+(v^4)))^3) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (27-81 (v^4)-48 (Sqrt[3]) (v^6)-27 (v^8)+(v^12)) Log[(3^(1/4))-v])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (27-81 (v^4)-48 (Sqrt[3]) (v^6)-27 (v^8)+(v^12)) Log[(3^(1/4))+v])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))+((v (-3+(v^4)) (3+4 (Sqrt[3]) (v^2)+(v^4)) Log[(Sqrt[3])+(v^2)])/((Sqrt[2]) (3^(3/4)) (((3+(v^4)))^2) (3+2 (Sqrt[3]) (v^2)+(v^4))))-((v (9-18 (v^4)+(v^8)) Log[3+(v^4)])/((Sqrt[2]) (3^(3/4)) (-3+(v^4)) (((3+(v^4)))^2)));

bFG3vNEWS[v_]=Normal[(Simplify/@Series[(bFG3'[v]/.Flatten[Solve[eqnFG2o3==0,bFG3'[v]]//Expand])//.Union[subsSOLFGwDERo012,{dFG3[v]->Integrate[Series[dFG3vNEW[v],{v,0,100}],v],dFG3'[v]->dFG3vNEW[v],dFG3''[v]->dFG3vNEW'[v],aFG3'[v]->aFG3vNEW[v]}]//Expand,{v,0,80}])//.Log[ah_Integer]->xxx[ah]];

aFG3NEWS[v_]=Normal[(Simplify/@Integrate[Series[aFG3vNEW[v],{v,0,100}],v])//.Log[ah_Integer]->xxx[ah]];

dFG3NEWS[v_]=Normal[(Simplify/@Integrate[Series[dFG3vNEW[v],{v,0,100}],v])//.Log[ah_Integer]->xxx[ah]];

bFG3vNEWS[v_]=-(7/81) (4 (Sqrt[2]) (3^(3/4))-3 DFG3a) (v^3)-((70 (Sqrt[2]) (v^9))/(243 (3^(3/4))))+((922 (Sqrt[2]) (v^13))/(3645 (3^(3/4))))-((296 (Sqrt[2]) (v^17))/(8505 (3^(3/4))))+((165224 (Sqrt[2]) (v^21))/(2066715 (3^(3/4))))-((31154 (Sqrt[2]) (v^25))/(22733865 (3^(3/4))))+((45673066 (Sqrt[2]) (v^29))/(2659862205 (3^(3/4))))+((794432 (Sqrt[2]) (v^33))/(1899901575 (3^(3/4))))+((1263854624 (Sqrt[2]) (v^37))/(406958917365 (3^(3/4))))+((607783658 (Sqrt[2]) (v^41))/(4295677461075 (3^(3/4))))+((247791750226 (Sqrt[2]) (v^45))/(487129824085905 (3^(3/4))))+((34004099048 (Sqrt[2]) (v^49))/(1143263872854675 (3^(3/4))))+((15140405890856 (Sqrt[2]) (v^53))/(193915141511119875 (3^(3/4))))+((10198310998514 (Sqrt[2]) (v^57))/(1944691847725802175 (3^(3/4))))+((7530352660734182 (Sqrt[2]) (v^61))/(657954075147229735875 (3^(3/4))))+((13221745070528704 (Sqrt[2]) (v^65))/(15734501739949465397925 (3^(3/4))))+((3273184777370143232 (Sqrt[2]) (v^69))/(2019261056626848059400375 (3^(3/4))))+((125547754119353866 (Sqrt[2]) (v^73))/(991273609616816320069275 (3^(3/4))))+((150305558090323527574 (Sqrt[2]) (v^77))/(672413931856740403780324875 (3^(3/4))))-((2 (v^39) (1575 DFG3a+2 (Sqrt[2]) (3^(3/4)) (-33075-5250 Log[2])))/167403915)-((4 (v^47) (945 DFG3a+4 (Sqrt[2]) (3^(3/4)) (-14385-1890 Log[2])))/1506635235)+(((v^75) (75 DFG3a+4 (Sqrt[2]) (3^(3/4)) (-2863-234 Log[2])))/31381059609)+(((v^67) (69 DFG3a+4 (Sqrt[2]) (3^(3/4)) (-2095-192 Log[2])))/3486784401)+(((v^59) (63 DFG3a+4 (Sqrt[2]) (3^(3/4)) (-1477-154 Log[2])))/387420489)+((8 (v^31) (-3 DFG3a+16 (Sqrt[2]) (3^(3/4)) (5+Log[2])))/177147)+(2/243) (v^7) (-3 DFG3a+2 (Sqrt[2]) (3^(3/4)) (3+2 Log[2]))+((4 (v^15) (-3 DFG3a+4 (Sqrt[2]) (3^(3/4)) (5+2 Log[2])))/2187)+(1/729) (v^11) (27 DFG3a-4 (Sqrt[2]) (3^(3/4)) (23+10 Log[2]))+((14 (v^55) (-3 DFG3a+2 (Sqrt[2]) (3^(3/4)) (125+14 Log[2])))/129140163)+(((v^19) (33 DFG3a-4 (Sqrt[2]) (3^(3/4)) (77+24 Log[2])))/6561)+(((v^43) (17 DFG3a-4 (Sqrt[2]) (3^(3/4)) (209+30 Log[2])))/1594323)+(((v^51) (19 DFG3a-4 (Sqrt[2]) (3^(3/4)) (331+40 Log[2])))/14348907)+(((v^27) (39 DFG3a-4 (Sqrt[2]) (3^(3/4)) (185+42 Log[2])))/59049)+(((v^35) (45 DFG3a-4 (Sqrt[2]) (3^(3/4)) (363+64 Log[2])))/531441)+((2 (v^23) (-45 DFG3a+2 (Sqrt[2]) (3^(3/4)) (335+90 Log[2])))/98415)-((2 (v^71) (36855 DFG3a+2 (Sqrt[2]) (3^(3/4)) (-561386 Log[2]+7 (-365625+48608 Log[2]))))/14278382122095)-((16 (v^63) (4095 DFG3a+(Sqrt[2]) (3^(3/4)) (-128744 Log[2]+7 (3780 Log[2]+13 (-4920+644 Log[2])))))/1586486902455)-((4 (v^79) (389025 DFG3a+4 (Sqrt[2]) (3^(3/4)) (-3650066 Log[2]+7 (71820 Log[2]+13 (-183825+20336 Log[2])))))/2441603342878245);

bFG3NEWS[v_]=Integrate[bFG3vNEWS[v],v];

Initialization

The KMNO metric ansatz

ds2EF=2dt dr-(r^2)AEF[t,r](dt^2)+(((1+r t))^2)Exp[bEF[t,r]](dy^2)+(r^2)Exp[cEF[t,r]]((dx1^2)+(dx2^2));

Coordinate transformation defined perturbatively in (1/(τ^(2/3)))expansion

t[τ_,z_]=τ(t0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))t1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))t2[(z/(τ^(1/3)))]+(1/(τ^2))t3[(z/(τ^(1/3)))]+(1/(τ^(8/3)))t4[(z/(τ^(1/3)))]);
r[τ_,z_]=(1/z)(r0[(z/(τ^(1/3)))]+(1/(τ^(2/3)))r1[(z/(τ^(1/3)))]+(1/(τ^(4/3)))r2[(z/(τ^(1/3)))]+(1/(τ^2))r3[(z/(τ^(1/3)))]+(1/(τ^(8/3)))r4[(z/(τ^(1/3)))]);

Warp factors

AEF[y_,x_]=AEF0[x (y^(1/3))]+(1/(y^(2/3)))AEF1[x (y^(1/3))]+(1/(y^(4/3)))AEF2[x (y^(1/3))]+(1/(y^2))AEF3[x (y^(1/3))];
bEF[y_,x_]=bEF0[x (y^(1/3))]+(1/(y^(2/3)))bEF1[x (y^(1/3))]+(1/(y^(4/3)))bEF2[x (y^(1/3))]+(1/(y^2))bEF3[x (y^(1/3))];
cEF[y_,x_]=cEF0[x (y^(1/3))]+(1/(y^(2/3)))cEF1[x (y^(1/3))]+(1/(y^(4/3)))cEF2[x (y^(1/3))]+(1/(y^2))cEF3[x (y^(1/3))];

Transformed metric

ds2Expand=Expand[Expand[ds2EF/.{t->t[τ,z],r->r[τ,z],dt->D[t[τ,z],τ]dτ+D[t[τ,z],z]dz,dr->D[r[τ,z],τ]dτ+D[r[τ,z],z]dz}]//.{z->v (τ^(1/3)),τ->(u^(-3/2)),((((u^(ah_))))^(bh_))->(u^(ah bh)),(((((t0[v]+u t1[v]+(u^2) t2[v]+(u^3) t3[v])/(u^(3/2)))))^(1/3))->(1/(Sqrt[u]))(((t0[v]+u t1[v]+(u^2) t2[v]+(u^3) t3[v]))^(1/3))}];

Different terms in the transformed metric

ds2Series=Series[ds2Expand,{u,0,5}];

dτdτ=Expand/@Series[D[Normal[(1/u)ds2Series]//.dτ dτ->yyy,yyy],{u,0,3}];

dydy=Expand/@Series[D[Normal[(u^2)ds2Series]//.dy dy->yyy,yyy],{u,0,3}];

dx1dx1=Expand/@Series[D[Normal[(1/u)ds2Series]//.dx1 dx1->yyy,yyy],{u,0,3}];

dzdτ=Expand/@Series[D[Normal[(1/u)ds2Series]//.dz dτ->yyy,yyy],{u,0,4}];

dzdz=Expand/@Series[D[Normal[(1/u)ds2Series]//.(dz^2)->yyy,yyy],{u,0,4}];

bEF0[v_]=0;
cEF0[v_]=0;

t0[v_]=1;

SeriesCoefficient[dzdτ,0]

Flatten[Solve[{SeriesCoefficient[dzdz,0]==(1/(v^2)),SeriesCoefficient[dzdτ,0]==0},{t1'[v],r0'[v]}]]//Simplify

subs01={r0'[v]->-(((-1+(Sqrt[AEF0[((r0[v])/v)]])) r0[v])/v),t1'[v]->-(1/((Sqrt[AEF0[((r0[v])/v)]]) r0[v]))};
subsAEF0={AEF0'[ah_]->(4/ah)-((4 AEF0[ah])/ah),AEF0''[ah_]->-(4/(ah^2))+((4 AEF0[ah])/(ah^2))-((4 AEF0'[ah])/ah),Derivative[3][AEF0][ah_]->(8/(ah^3))-((8 AEF0[ah])/(ah^3))+((8 AEF0'[ah])/(ah^2))-((4 AEF0''[ah])/ah),Derivative[4][AEF0][ah_]->-(24/(ah^4))+((24 AEF0[ah])/(ah^4))-((24 AEF0'[ah])/(ah^3))+((12 AEF0''[ah])/(ah^2))-((4 Derivative[3][AEF0][ah])/ah),Derivative[5][AEF0][ah_]->(96/(ah^5))-((96 AEF0[ah])/(ah^5))+((96 AEF0'[ah])/(ah^4))-((48 AEF0''[ah])/(ah^3))+((16 Derivative[3][AEF0][ah])/(ah^2))-((4 Derivative[4][AEF0][ah])/ah)};

Flatten[Solve[{SeriesCoefficient[dzdz,1]==0,SeriesCoefficient[dzdτ,1]==0},{t2'[v],r1'[v]}]]//.subs01//Simplify

subs12={t2'[v]->((-2 v (Sqrt[AEF0[((r0[v])/v)]])+3 AEF1[((r0[v])/v)] r0[v]-2 AEF0[((r0[v])/v)] (3 r1[v]+2 r0[v] t1[v])+2 (v+6 r1[v]+2 r0[v] t1[v]))/(6 ((AEF0[((r0[v])/v)])^(3/2)) ((r0[v])^2))),r1'[v]->((-3 AEF1[((r0[v])/v)] r0[v]+6 (-2+(Sqrt[AEF0[((r0[v])/v)]])+AEF0[((r0[v])/v)]) r1[v]+4 (-1+AEF0[((r0[v])/v)]) r0[v] t1[v])/(6 v (Sqrt[AEF0[((r0[v])/v)]])))};

Flatten[Solve[{SeriesCoefficient[dzdz,2]==0,SeriesCoefficient[dzdτ,2]==0},{t3'[v],r2'[v]}]]//.Union[subsAEF0,subs01,subs12]//Simplify

subs23={t3'[v]->(1/(72 v ((AEF0[((r0[v])/v)])^(5/2)) ((r0[v])^3)))(-24 (v^2) ((AEF0[((r0[v])/v)])^(3/2)) (2 r1[v]+r0[v] t1[v])+8 (v^2) (Sqrt[AEF0[((r0[v])/v)]]) (3 AEF1[((r0[v])/v)] r0[v]+2 (v+6 r1[v]+2 r0[v] t1[v]))-3 v (((3 AEF1[((r0[v])/v)] r0[v]+2 (v+6 r1[v]+2 r0[v] t1[v])))^2)+8 v ((AEF0[((r0[v])/v)])^2) r0[v] (-9 r2[v]-6 r1[v] t1[v]+r0[v] (((t1[v])^2)-6 t2[v]))+4 AEF0[((r0[v])/v)] (-(v^3)+9 v AEF2[((r0[v])/v)] ((r0[v])^2)+90 v ((r1[v])^2)+36 v r0[v] r2[v]+10 (v^2) r0[v] t1[v]+12 v AEF1[((r0[v])/v)] ((r0[v])^2) t1[v]+10 v ((r0[v])^2) ((t1[v])^2)+12 v ((r0[v])^2) t2[v]+3 ((r0[v])^3) t1[v] AEF1'[((r0[v])/v)]+r1[v] (36 (v^2)+45 v AEF1[((r0[v])/v)] r0[v]+84 v r0[v] t1[v]+9 ((r0[v])^2) AEF1'[((r0[v])/v)]))),r2'[v]->(1/(72 (v^2) ((AEF0[((r0[v])/v)])^(3/2)) r0[v]))(8 (v^3) (Sqrt[AEF0[((r0[v])/v)]])+72 v ((AEF0[((r0[v])/v)])^(3/2)) r0[v] r2[v]+v (-4 (v^2)+9 ((AEF1[((r0[v])/v)])^2) ((r0[v])^2)+144 ((r1[v])^2)+96 r0[v] r1[v] t1[v]+16 ((r0[v])^2) ((t1[v])^2)+24 AEF1[((r0[v])/v)] r0[v] (3 r1[v]+r0[v] t1[v]))-8 v ((AEF0[((r0[v])/v)])^2) (9 ((r1[v])^2)+6 r0[v] r1[v] t1[v]+r0[v] (-9 r2[v]+5 r0[v] ((t1[v])^2)-6 r0[v] t2[v]))-4 AEF0[((r0[v])/v)] ((v^3)+9 v AEF2[((r0[v])/v)] ((r0[v])^2)+27 v AEF1[((r0[v])/v)] r0[v] r1[v]+18 v ((r1[v])^2)+36 v r0[v] r2[v]+12 v r0[v] r1[v] t1[v]-6 v ((r0[v])^2) ((t1[v])^2)+12 v ((r0[v])^2) t2[v]+9 ((r0[v])^2) r1[v] AEF1'[((r0[v])/v)]+3 ((r0[v])^3) t1[v] AEF1'[((r0[v])/v)]))};

Solve[(SeriesCoefficient[dzdz,3]//.Union[subsAEF0,subs01,subs12,subs23]//Expand//Simplify)==0,r3'[v]]//Expand//Simplify

subsr3={r3'[v]->(1/(1296 (v^3) ((AEF0[((r0[v])/v)])^(5/2)) ((r0[v])^2)))(1296 (v^2) ((AEF0[((r0[v])/v)])^(5/2)) ((r0[v])^2) r3[v]+48 (v^4) ((AEF0[((r0[v])/v)])^(3/2)) (15 r1[v]+2 r0[v] t1[v])-48 (v^4) (Sqrt[AEF0[((r0[v])/v)]]) (3 AEF1[((r0[v])/v)] r0[v]+2 (v+6 r1[v]+2 r0[v] t1[v]))+3 (v^2) (-3 AEF1[((r0[v])/v)] r0[v]+4 (v-3 r1[v]-r0[v] t1[v])) (((3 AEF1[((r0[v])/v)] r0[v]+2 (v+6 r1[v]+2 r0[v] t1[v])))^2)+16 (v^2) ((AEF0[((r0[v])/v)])^3) (81 ((r1[v])^3)+54 r0[v] ((r1[v])^2) t1[v]+9 r0[v] r1[v] (-18 r2[v]+r0[v] (5 ((t1[v])^2)-6 t2[v]))+((r0[v])^2) (81 r3[v]-54 r2[v] t1[v]+2 r0[v] (20 ((t1[v])^3)-45 t1[v] t2[v]+27 t3[v])))+6 v AEF0[((r0[v])/v)] (9 v ((AEF1[((r0[v])/v)])^2) ((r0[v])^2) (21 r1[v]+2 r0[v] t1[v])+6 AEF1[((r0[v])/v)] r0[v] ((v^3)+9 v AEF2[((r0[v])/v)] ((r0[v])^2)+162 v ((r1[v])^2)+36 v r0[v] r2[v]+2 v ((r0[v])^2) ((t1[v])^2)+12 v ((r0[v])^2) t2[v]+3 ((r0[v])^3) t1[v] AEF1'[((r0[v])/v)]+3 r0[v] r1[v] (28 v t1[v]+3 r0[v] AEF1'[((r0[v])/v)]))+4 (216 v ((r1[v])^3)+18 r0[v] ((r1[v])^2) (14 v t1[v]+3 r0[v] AEF1'[((r0[v])/v)])+3 r1[v] (-7 (v^3)+18 v AEF2[((r0[v])/v)] ((r0[v])^2)+72 v r0[v] r2[v]+8 v ((r0[v])^2) (2 ((t1[v])^2)+3 t2[v])+12 ((r0[v])^3) t1[v] AEF1'[((r0[v])/v)])+2 ((v^4)-(v^3) r0[v] t1[v]+36 v ((r0[v])^2) r2[v] t1[v]+v ((r0[v])^3) t1[v] (9 AEF2[((r0[v])/v)]-2 ((t1[v])^2)+12 t2[v])+3 ((r0[v])^4) ((t1[v])^2) AEF1'[((r0[v])/v)])))-4 ((AEF0[((r0[v])/v)])^2) (162 (v^2) AEF3[((r0[v])/v)] ((r0[v])^3)+324 (v^2) ((r1[v])^3)+18 r1[v] ((v^4)+27 (v^2) AEF2[((r0[v])/v)] ((r0[v])^2)+36 (v^2) r0[v] r2[v]+2 (v^2) ((r0[v])^2) (((t1[v])^2)+6 t2[v])+3 v ((r0[v])^3) (4 t1[v] AEF1'[((r0[v])/v)]+3 AEF2'[((r0[v])/v)])+3 ((r0[v])^4) t1[v] AEF1''[((r0[v])/v)])+((r0[v])^2) (486 (v^2) AEF1[((r0[v])/v)] r2[v]+648 (v^2) r3[v]-108 (v^2) AEF2[((r0[v])/v)] r0[v] t1[v]+216 (v^2) r2[v] t1[v]+88 (v^2) r0[v] ((t1[v])^3)-216 (v^2) r0[v] t1[v] t2[v]+216 (v^2) r0[v] t3[v]+162 v r0[v] r2[v] AEF1'[((r0[v])/v)]-18 v ((r0[v])^2) ((t1[v])^2) AEF1'[((r0[v])/v)]+54 v ((r0[v])^2) t2[v] AEF1'[((r0[v])/v)]+54 v ((r0[v])^2) t1[v] AEF2'[((r0[v])/v)]+9 ((r0[v])^3) ((t1[v])^2) AEF1''[((r0[v])/v)])+27 r0[v] ((r1[v])^2) (18 (v^2) AEF1[((r0[v])/v)]+16 (v^2) t1[v]+3 r0[v] (6 v AEF1'[((r0[v])/v)]+r0[v] AEF1''[((r0[v])/v)]))))};

subsTRAFO=Union[subs01,subs12,subs23,subsr3];

checko0=subs01[[1]]/.Rule[ah_,bh_]->ah-bh;

checko1=Expand[{subs01[[2]],subs12[[2]]}/.Rule[ah_,bh_]->ah-bh];

checko2=Expand[{subs12[[1]],subs23[[2]]}/.Rule[ah_,bh_]->ah-bh];

checko3=Expand[{subs23[[1]],subsr3[[1]]}/.Rule[ah_,bh_]->ah-bh];

ORDERS 0 - 2

ORDER 0

Calculating r0[v] (t0[v] is set to 1)

Solve[SeriesCoefficient[Simplify/@Series[dx1dx1-(1/(v^2))Exp[cFG0[v]+u cFG1[v]+(u^2)cFG2[v]+(u^3)cFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],0]==0,r0[v]]

r0[v_]=(E^((cFG0[v])/2));

w=((3^(1/4))/(Sqrt[2]));

order 1

Calculating r1[v] and t1[v]

Solve[{SeriesCoefficient[Simplify/@Series[dx1dx1-(1/(v^2))Exp[cFG0[v]+u cFG1[v]+(u^2)cFG2[v]+(u^3)cFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],1]==0,SeriesCoefficient[Simplify/@Series[dτdτ+(1/(v^2))Exp[aFG0[v]+u aFG1[v]+(u^2)aFG2[v]+(u^3)aFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],1]==0},{r1[v],t1[v]}]//Expand//Simplify

t1[v_]=-(1/(4-2 AEF0[((E^((cFG0[v])/2))/v)]))(2 (E^(-((cFG0[v])/2))) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]])+3 AEF1[((E^((cFG0[v])/2))/v)]-3 (E^(aFG0[v]-cFG0[v])) aFG1[v]-6 cEF1[((E^((cFG0[v])/2))/v)]+3 AEF0[((E^((cFG0[v])/2))/v)] (cEF1[((E^((cFG0[v])/2))/v)]-cFG1[v])+6 cFG1[v]+(E^(-((cFG0[v])/2))) (v^2) cFG0'[v]);

r1[v_]=(1/2) (E^((cFG0[v])/2)) (-cEF1[((E^((cFG0[v])/2))/v)]+cFG1[v]);

Transformation check in orders 0 and 1

Expand/@Assuming[And[v>0,v<(3^(1/4))],Series[(SeriesCoefficient[Simplify/@Series[dydy-(1/(v^2))Exp[bFG0[v]+u bFG1[v]+(u^2)bFG2[v]+(u^3)bFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],1]//Expand)//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v]],{v,0,100}]]//N//Chop

Series[checko0//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v]],{v,0,60}]

Simplify//@Series[checko1//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v]],{v,0,30}]//.Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0

order 2

Calculating r2[v] and t2[v]

Solve[{SeriesCoefficient[Series[dx1dx1-(1/(v^2))Exp[cFG0[v]+u cFG1[v]+(u^2)cFG2[v]+(u^3)cFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],2]==0,SeriesCoefficient[Series[dydy-(1/(v^2))Exp[bFG0[v]+u bFG1[v]+(u^2)bFG2[v]+(u^3)bFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],2]==0},{r2[v],t2[v]}]//Expand//Simplify

r2[v_]=Expand[(1/(24 v (-2+AEF0[((E^((cFG0[v])/2))/v)])))(E^(-((cFG0[v])/2))) (3 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] (5 ((cEF1[((E^((cFG0[v])/2))/v)])^2)-4 cEF2[((E^((cFG0[v])/2))/v)]-6 cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+((cFG1[v])^2)+4 cFG2[v])+(Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) (8 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]-4 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)])-2 (15 (E^(cFG0[v])) v ((cEF1[((E^((cFG0[v])/2))/v)])^2)-12 (E^(cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)]-18 (E^(cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+3 (E^(cFG0[v])) v ((cFG1[v])^2)+12 (E^(cFG0[v])) v cFG2[v]+3 (E^(aFG0[v])) aFG1[v] (2 v cEF1[((E^((cFG0[v])/2))/v)]-(E^((cFG0[v])/2)) cEF1'[((E^((cFG0[v])/2))/v)])+3 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (-2 v cEF1[((E^((cFG0[v])/2))/v)]+(E^((cFG0[v])/2)) cEF1'[((E^((cFG0[v])/2))/v)])-2 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+(E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]))];

t2[v_]=Expand[(1/(24 v (((-2+AEF0[((E^((cFG0[v])/2))/v)]))^2)))(E^(-2 cFG0[v])) (-48 (E^(cFG0[v])) (v^3)-27 (E^(2 cFG0[v])) v ((AEF1[((E^((cFG0[v])/2))/v)])^2)-72 (E^(aFG0[v]+((cFG0[v])/2))) (v^2) aFG1[v]-27 (E^(2 aFG0[v])) v ((aFG1[v])^2)-96 (E^((3 cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]-48 (E^(aFG0[v]+cFG0[v])) v aFG1[v] bEF1[((E^((cFG0[v])/2))/v)]-24 (E^(2 cFG0[v])) v ((bEF1[((E^((cFG0[v])/2))/v)])^2)-48 (E^(2 cFG0[v])) v bEF2[((E^((cFG0[v])/2))/v)]+24 (E^(bFG0[v]+cFG0[v])) v ((bFG1[v])^2)+48 (E^(bFG0[v]+cFG0[v])) v bFG2[v]-96 (E^((3 cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]-60 (E^(aFG0[v]+cFG0[v])) v aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]-48 (E^(2 cFG0[v])) v bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-36 (E^(2 cFG0[v])) v ((cEF1[((E^((cFG0[v])/2))/v)])^2)+48 (E^(2 cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)]+96 (E^((3 cFG0[v])/2)) (v^2) cFG1[v]+36 (E^(aFG0[v]+cFG0[v])) v aFG1[v] cFG1[v]+48 (E^(2 cFG0[v])) v bEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+24 (E^(2 cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+12 (E^(2 cFG0[v])) v ((cFG1[v])^2)-48 (E^(2 cFG0[v])) v cFG2[v]-3 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) (4 (v^2)+2 (E^(cFG0[v])) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+4 (E^(cFG0[v])) bEF2[((E^((cFG0[v])/2))/v)]-2 (E^(bFG0[v])) ((bFG1[v])^2)-4 (E^(bFG0[v])) bFG2[v]+8 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]+3 (E^(cFG0[v])) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-4 (E^(cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)]-8 (E^((cFG0[v])/2)) v cFG1[v]-2 (E^(cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-(E^(cFG0[v])) ((cFG1[v])^2)+bEF1[((E^((cFG0[v])/2))/v)] (8 (E^((cFG0[v])/2)) v+4 (E^(cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)]-4 (E^(cFG0[v])) cFG1[v])+4 (E^(cFG0[v])) cFG2[v])-12 (E^(aFG0[v]+((3 cFG0[v])/2))) aFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+12 (E^(aFG0[v]+((3 cFG0[v])/2))) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) (6 (v^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)]+5 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-3 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+24 (E^(cFG0[v])) (v^4) cFG0'[v]+18 (E^(aFG0[v]+((cFG0[v])/2))) (v^3) aFG1[v] cFG0'[v]+16 (E^((3 cFG0[v])/2)) (v^3) bEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+20 (E^((3 cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-12 (E^((3 cFG0[v])/2)) (v^3) cFG1[v] cFG0'[v]+4 (E^(2 cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-4 (E^(2 cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-3 (E^(cFG0[v])) (v^5) ((cFG0'[v])^2)+6 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (9 (E^(aFG0[v])) v aFG1[v]+(E^((cFG0[v])/2)) (12 (v^2)+8 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)]+10 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-6 (E^((cFG0[v])/2)) v cFG1[v]+2 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-2 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-3 (v^3) cFG0'[v]))+4 (E^((cFG0[v])/2)) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) (-9 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)]+9 (E^(aFG0[v])) v aFG1[v]+(E^((cFG0[v])/2)) (12 (v^2)+8 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)]+10 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-6 (E^((cFG0[v])/2)) v cFG1[v]+2 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-2 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-3 (v^3) cFG0'[v]))-2 AEF0[((E^((cFG0[v])/2))/v)] (3 (E^((3 cFG0[v])/2)) AEF1[((E^((cFG0[v])/2))/v)] (6 (v^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)]+5 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-3 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])-3 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] (6 (v^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)]+5 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-3 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+(E^(cFG0[v])) v (-18 (v^2)-12 (E^(cFG0[v])) ((bEF1[((E^((cFG0[v])/2))/v)])^2)-24 (E^(cFG0[v])) bEF2[((E^((cFG0[v])/2))/v)]+12 (E^(bFG0[v])) ((bFG1[v])^2)+24 (E^(bFG0[v])) bFG2[v]-48 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-18 (E^(cFG0[v])) ((cEF1[((E^((cFG0[v])/2))/v)])^2)+24 (E^(cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)]+48 (E^((cFG0[v])/2)) v cFG1[v]+12 (E^(cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+6 (E^(cFG0[v])) ((cFG1[v])^2)-24 (E^(cFG0[v])) cFG2[v]+6 (v^3) cFG0'[v]+5 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-3 (E^((cFG0[v])/2)) (v^2) cFG1[v] cFG0'[v]+(E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-(E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-4 (E^((cFG0[v])/2)) bEF1[((E^((cFG0[v])/2))/v)] (6 (E^((cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)]-6 (E^((cFG0[v])/2)) cFG1[v]+v (12-v cFG0'[v])))))];

Transformation check in the 2 order

Checking dτdτ warp factor transformation rules

testdτdτo2p0=Simplify/@(Simplify/@(Series[((Expand[SeriesCoefficient[Series[dτdτ+(1/(v^2))Exp[aFG0[v]+u aFG1[v]+(u^2)aFG2[v]+(u^3)aFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],2]]//Simplify)//.{AEF2[((E^((cFG0[v])/2))/v)]->0,bEF2[((E^((cFG0[v])/2))/v)]->0,cEF2[((E^((cFG0[v])/2))/v)]->0})//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v]],{v,0,20}]//.Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0)//.{Log[ah_Integer]->xxx[ah],Log[Times[Power[ah_Integer,bh_],Power[ch_Integer,dh_]]]->bh Log[ah]+dh Log[ch],Log[((Sqrt[3])/2)]->(1/2)Log[3]-Log[2],Log[Rational[ah_Integer,bh_Integer]]->Log[ah]-Log[bh]})

cEF2[v_]=dEF2[v]-(1/2)bEF2[v];

testdτdτo2p1=Simplify/@(Series[-((3+(v^4))/(3 (v^2)))AEF2[((E^((cFG0[v])/2))/v)]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v]]//Simplify,{v,0,20}]//.Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0)

testdτdτo2p2=Simplify/@((Simplify/@(Series[-((((-3+(v^4)))^2)/(3 (v^2) (3+(v^4))))bEF2[((E^((cFG0[v])/2))/v)]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.{Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0,Floor[((π+Arg[v]-Arg[I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[(Sqrt[3])-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-(1/2) Arg[3+(v^4)])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[(1+I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1+I) ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[-(Sqrt[3])+(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1}))//.Union[subsCOMBO,{Log[ah_Integer]->xxx[ah],Log[Times[Power[ah_Integer,bh_],Power[ch_Integer,dh_]]]->bh Log[ah]+dh Log[ch],Log[((Sqrt[3])/2)]->(1/2)Log[3]-Log[2],Log[Rational[ah_Integer,bh_Integer]]->Log[ah]-Log[bh]}])

testdτdτo2p3=Simplify/@(Series[((4 (3+(v^4)))/(9 (v^2))) dEF2[((E^((cFG0[v])/2))/v)]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0)

SUM OF ALL EXPRESSIONS FROM ABOVE :

testdτdτo2p0+testdτdτo2p1+testdτdτo2p2+testdτdτo2p3

This part works in the 2 order!!!

Checking dτdz and (dz^2) transformations

subsFLOOR={Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0,Floor[((π+Arg[v]-Arg[I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[(Sqrt[3])-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-(1/2) Arg[3+(v^4)])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[(1+I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1+I) ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[-(Sqrt[3])+(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1};

checko2rp1=Simplify/@(Series[checko2[[1]][[Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp2=Simplify/@(Series[checko2[[1]][[50+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp3=Simplify/@(Series[checko2[[1]][[100+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp4=Simplify/@(Series[checko2[[1]][[150+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp5=Simplify/@(Series[checko2[[1]][[200+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp6=Simplify/@(Series[checko2[[1]][[250+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp7=Simplify/@(Series[checko2[[1]][[300+Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp8=Simplify/@(Series[checko2[[1]][[350+Range[60]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2tp1=Simplify/@(Series[checko2[[2]][[Range[50]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2tp2=Simplify/@(Series[checko2[[2]][[50+Range[46]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)

checko2rp1+checko2rp2+checko2rp3+checko2rp4+checko2rp5+checko2rp6+checko2rp7+checko2rp8

checko2tp1+checko2tp2

BOTH WORKS. The transformation works then in the second order too.

ORDER 3

In the third order it is preferable to use dEF3[v] and dFG3[v] instead of cEF3[v] and cFG3[v] respectively.

cEF3[v_]=dEF3[v]-(1/2)bEF3[v];

cEF2[v_]=dEF2[v]-(1/2)bEF2[v];

cFG3[v_]=dFG3[v]-(1/2)bFG3[v];

(Flatten[Solve[{SeriesCoefficient[Series[dx1dx1-(1/(v^2))Exp[cFG0[v]+u cFG1[v]+(u^2)cFG2[v]+(u^3)cFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],3]==0,SeriesCoefficient[Series[dydy-(1/(v^2))Exp[bFG0[v]+u bFG1[v]+(u^2)bFG2[v]+(u^3)bFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],3]==0},{r3[v],t3[v]}]//Expand]//Simplify)[[2]]

r3[v_]=-(1/(144 (v^2) (((-2+AEF0[((E^((cFG0[v])/2))/v)]))^2)))(-36 (E^((cFG0[v])/2)) (v^2) (((-2+AEF0[((E^((cFG0[v])/2))/v)]))^2) bEF3[((E^((cFG0[v])/2))/v)]+36 (E^((cFG0[v])/2)) (v^2) (((-2+AEF0[((E^((cFG0[v])/2))/v)]))^2) bFG3[v]+96 (E^(-((cFG0[v])/2))) (v^4) cEF1[((E^((cFG0[v])/2))/v)]-96 (E^(-((cFG0[v])/2))) (v^4) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1[((E^((cFG0[v])/2))/v)]-32 (E^(-((cFG0[v])/2))) (v^4) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+48 (E^(-((cFG0[v])/2))) (v^4) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF1[((E^((cFG0[v])/2))/v)]+24 (E^(-((cFG0[v])/2))) (v^4) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]-144 (v^3) AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+192 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+72 (v^3) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+144 (E^((cFG0[v])/2)) (v^2) ((AEF1[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]+144 (E^(aFG0[v]-cFG0[v])) (v^3) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]-192 (E^(aFG0[v]-cFG0[v])) (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]-72 (E^(aFG0[v]-cFG0[v])) (v^3) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]-288 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF1[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]+144 (E^(2 aFG0[v]-((3 cFG0[v])/2))) (v^2) ((aFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]+192 (v^3) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-64 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-192 (v^3) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+32 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+48 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-96 (E^((cFG0[v])/2)) (v^2) AEF1[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+48 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+96 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-48 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+48 (E^((cFG0[v])/2)) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]-48 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]+12 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]+96 (E^((cFG0[v])/2)) (v^2) bEF2[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bEF2[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF2[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-48 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]+48 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]-12 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]-96 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]+96 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]-24 (E^(bFG0[v]-((cFG0[v])/2))) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]+192 (v^3) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-368 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-192 (v^3) AEF0[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+184 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) ((cEF1[((E^((cFG0[v])/2))/v)])^2)+48 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-552 (E^((cFG0[v])/2)) (v^2) AEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+276 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+552 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) aFG1[v] ((cEF1[((E^((cFG0[v])/2))/v)])^2)-276 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+96 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)-96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)+588 (E^((cFG0[v])/2)) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^3)-588 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^3)+147 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((cEF1[((E^((cFG0[v])/2))/v)])^3)+192 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF2[((E^((cFG0[v])/2))/v)]-96 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF2[((E^((cFG0[v])/2))/v)]+288 (E^((cFG0[v])/2)) (v^2) AEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-144 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-288 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) aFG1[v] cEF2[((E^((cFG0[v])/2))/v)]+144 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF2[((E^((cFG0[v])/2))/v)]-816 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]+816 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-204 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-192 (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+336 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+192 (v^3) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-168 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-48 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+504 (E^((cFG0[v])/2)) (v^2) AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-252 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-504 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+252 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-96 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-1092 (E^((cFG0[v])/2)) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]+1092 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]-273 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]+720 (E^((cFG0[v])/2)) (v^2) cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]-720 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]+180 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]+516 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)-516 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)+129 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)-12 (E^((cFG0[v])/2)) (v^2) ((cFG1[v])^3)+12 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((cFG1[v])^3)-3 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((cFG1[v])^3)+240 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]-240 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]+60 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]-144 (E^((cFG0[v])/2)) (v^2) cFG1[v] cFG2[v]+144 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cFG1[v] cFG2[v]-36 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cFG1[v] cFG2[v]+288 (E^((cFG0[v])/2)) (v^2) dEF3[((E^((cFG0[v])/2))/v)]-288 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] dEF3[((E^((cFG0[v])/2))/v)]+72 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) dEF3[((E^((cFG0[v])/2))/v)]-288 (E^((cFG0[v])/2)) (v^2) dFG3[v]+288 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] dFG3[v]-72 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) dFG3[v]-16 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+12 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(aFG0[v])) v aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-12 (E^(aFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-48 (v^3) cEF1'[((E^((cFG0[v])/2))/v)]+48 (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1'[((E^((cFG0[v])/2))/v)]+12 (v^3) AEF0[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF1'[((E^((cFG0[v])/2))/v)]-12 (v^3) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]+72 (E^((cFG0[v])/2)) (v^2) AEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-108 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) AEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-36 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-81 (E^(cFG0[v])) v ((AEF1[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]-72 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+108 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+36 (E^(aFG0[v]-((cFG0[v])/2))) (v^2) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+162 (E^(aFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-81 (E^(2 aFG0[v]-cFG0[v])) v ((aFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+32 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-16 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(aFG0[v])) v aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(aFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) v ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]-6 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(cFG0[v])) v bEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] bEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-12 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(bFG0[v])) v ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(bFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(bFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(bFG0[v])) v bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(bFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+12 (E^(bFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+152 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-76 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+228 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-114 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-228 (E^(aFG0[v])) v aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+114 (E^(aFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(cFG0[v])) v bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-12 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^(cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((cFG0[v])/2)) (v^2) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-168 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+84 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^2) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-252 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+126 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+252 (E^(aFG0[v])) v aFG1[v] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-126 (E^(aFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(cFG0[v])) v bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+12 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^(cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^(cFG0[v])) v ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^(cFG0[v])) v cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+24 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^2) cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(cFG0[v])) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+12 (E^((3 cFG0[v])/2)) AEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-6 (E^((3 cFG0[v])/2)) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-12 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(aFG0[v]+((cFG0[v])/2))) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+16 (E^(cFG0[v])) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)-8 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+24 (E^((3 cFG0[v])/2)) AEF1[((E^((cFG0[v])/2))/v)] ((cEF1'[((E^((cFG0[v])/2))/v)])^2)-12 (E^((3 cFG0[v])/2)) AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] ((cEF1'[((E^((cFG0[v])/2))/v)])^2)-24 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+12 (E^(aFG0[v]+((cFG0[v])/2))) AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] ((cEF1'[((E^((cFG0[v])/2))/v)])^2)-48 (E^((cFG0[v])/2)) (v^2) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF2'[((E^((cFG0[v])/2))/v)]+24 (E^((cFG0[v])/2)) (v^2) ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) cEF2'[((E^((cFG0[v])/2))/v)]-72 (E^(cFG0[v])) v AEF1[((E^((cFG0[v])/2))/v)] cEF2'[((E^((cFG0[v])/2))/v)]+36 (E^(cFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] AEF1[((E^((cFG0[v])/2))/v)] cEF2'[((E^((cFG0[v])/2))/v)]+72 (E^(aFG0[v])) v aFG1[v] cEF2'[((E^((cFG0[v])/2))/v)]-36 (E^(aFG0[v])) v AEF0[((E^((cFG0[v])/2))/v)] aFG1[v] cEF2'[((E^((cFG0[v])/2))/v)]-48 (E^(-((cFG0[v])/2))) (v^5) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+64 (E^(-((cFG0[v])/2))) (v^5) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+24 (E^(-((cFG0[v])/2))) (v^5) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+96 (v^4) AEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-96 (E^(aFG0[v]-cFG0[v])) (v^4) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-32 (v^4) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+16 (v^4) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-184 (v^4) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+92 (v^4) AEF0[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+96 (v^4) cEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]-48 (v^4) AEF0[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]+168 (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]-84 (v^4) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]-8 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+4 (E^((cFG0[v])/2)) (v^3) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+24 (v^4) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-36 (v^4) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-12 (v^4) AEF0[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-54 (E^((cFG0[v])/2)) (v^3) AEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+54 (E^(aFG0[v]-((cFG0[v])/2))) (v^3) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+16 (E^((cFG0[v])/2)) (v^3) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-8 (E^((cFG0[v])/2)) (v^3) AEF0[((E^((cFG0[v])/2))/v)] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+76 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-38 (E^((cFG0[v])/2)) (v^3) AEF0[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-84 (E^((cFG0[v])/2)) (v^3) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+42 (E^((cFG0[v])/2)) (v^3) AEF0[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+4 (E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-2 (E^(cFG0[v])) (v^2) AEF0[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^(cFG0[v])) (v^2) ((cEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-4 (E^(cFG0[v])) (v^2) AEF0[((E^((cFG0[v])/2))/v)] ((cEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-24 (E^((cFG0[v])/2)) (v^3) cEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]+12 (E^((cFG0[v])/2)) (v^3) AEF0[((E^((cFG0[v])/2))/v)] cEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]+16 (E^(-((cFG0[v])/2))) (v^6) cEF1[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)-9 (v^5) cEF1'[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)+4 (E^((cFG0[v])/2)) (v^2) AEF0[((E^((cFG0[v])/2))/v)] cEF1''[((E^((cFG0[v])/2))/v)]+12 (E^(cFG0[v])) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) AEF1[((E^((cFG0[v])/2))/v)] cEF1''[((E^((cFG0[v])/2))/v)]+9 (E^((3 cFG0[v])/2)) ((AEF1[((E^((cFG0[v])/2))/v)])^2) cEF1''[((E^((cFG0[v])/2))/v)]-12 (E^(aFG0[v])) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) aFG1[v] cEF1''[((E^((cFG0[v])/2))/v)]-18 (E^(aFG0[v]+((cFG0[v])/2))) AEF1[((E^((cFG0[v])/2))/v)] aFG1[v] cEF1''[((E^((cFG0[v])/2))/v)]+9 (E^(2 aFG0[v]-((cFG0[v])/2))) ((aFG1[v])^2) cEF1''[((E^((cFG0[v])/2))/v)]+4 (E^((cFG0[v])/2)) (v^3) (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]+6 (E^(cFG0[v])) (v^2) AEF1[((E^((cFG0[v])/2))/v)] cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]-6 (E^(aFG0[v])) (v^2) aFG1[v] cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]+(E^((cFG0[v])/2)) (v^4) ((cFG0'[v])^2) cEF1''[((E^((cFG0[v])/2))/v)]);

t3[v_]=(1/(144 (v^2) (((-2+AEF0[((E^((cFG0[v])/2))/v)]))^3)))(E^(-3 cFG0[v])) (-576 (E^((3 cFG0[v])/2)) (v^5)+243 (E^(3 cFG0[v])) (v^2) ((AEF1[((E^((cFG0[v])/2))/v)])^3)-1296 (E^(aFG0[v]+cFG0[v])) (v^4) aFG1[v]-972 (E^(2 aFG0[v]+((cFG0[v])/2))) (v^3) ((aFG1[v])^2)-243 (E^(3 aFG0[v])) (v^2) ((aFG1[v])^3)-960 (E^(2 cFG0[v])) (v^4) bEF1[((E^((cFG0[v])/2))/v)]-1728 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^3) aFG1[v] bEF1[((E^((cFG0[v])/2))/v)]-576 (E^(2 aFG0[v]+cFG0[v])) (v^2) ((aFG1[v])^2) bEF1[((E^((cFG0[v])/2))/v)]-480 (E^((5 cFG0[v])/2)) (v^3) ((bEF1[((E^((cFG0[v])/2))/v)])^2)-456 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] ((bEF1[((E^((cFG0[v])/2))/v)])^2)-96 (E^(3 cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^3)+576 (E^((5 cFG0[v])/2)) (v^3) bEF2[((E^((cFG0[v])/2))/v)]-144 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] bEF2[((E^((cFG0[v])/2))/v)]+192 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] bEF2[((E^((cFG0[v])/2))/v)]+864 (E^(3 cFG0[v])) (v^2) bEF3[((E^((cFG0[v])/2))/v)]+288 (E^(bFG0[v]+((3 cFG0[v])/2))) (v^3) ((bFG1[v])^2)+216 (E^(aFG0[v]+bFG0[v]+cFG0[v])) (v^2) aFG1[v] ((bFG1[v])^2)+192 (E^(bFG0[v]+2 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] ((bFG1[v])^2)-96 (E^(bFG0[v]+2 cFG0[v])) (v^2) ((bFG1[v])^3)+576 (E^(bFG0[v]+((3 cFG0[v])/2))) (v^3) bFG2[v]+432 (E^(aFG0[v]+bFG0[v]+cFG0[v])) (v^2) aFG1[v] bFG2[v]+384 (E^(bFG0[v]+2 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] bFG2[v]-576 (E^(bFG0[v]+2 cFG0[v])) (v^2) bFG1[v] bFG2[v]-288 (E^(3 cFG0[v])) (v^2) bFG3[v]-576 (E^(bFG0[v]+2 cFG0[v])) (v^2) bFG3[v]-1632 (E^(2 cFG0[v])) (v^4) cEF1[((E^((cFG0[v])/2))/v)]-2448 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^3) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)]-882 (E^(2 aFG0[v]+cFG0[v])) (v^2) ((aFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]-2304 (E^((5 cFG0[v])/2)) (v^3) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-1392 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]-624 (E^(3 cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1[((E^((cFG0[v])/2))/v)]-480 (E^(3 cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)]+240 (E^(bFG0[v]+2 cFG0[v])) (v^2) ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]+480 (E^(bFG0[v]+2 cFG0[v])) (v^2) bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]-1536 (E^((5 cFG0[v])/2)) (v^3) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-1068 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] ((cEF1[((E^((cFG0[v])/2))/v)])^2)-768 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] ((cEF1[((E^((cFG0[v])/2))/v)])^2)-456 (E^(3 cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^3)+144 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] cEF2[((E^((cFG0[v])/2))/v)]-192 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]+480 (E^(3 cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]+1440 (E^(2 cFG0[v])) (v^4) cFG1[v]+2160 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^3) aFG1[v] cFG1[v]+810 (E^(2 aFG0[v]+cFG0[v])) (v^2) ((aFG1[v])^2) cFG1[v]+1920 (E^((5 cFG0[v])/2)) (v^3) bEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+1296 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+528 (E^(3 cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]+288 (E^(3 cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)] cFG1[v]-144 (E^(bFG0[v]+2 cFG0[v])) (v^2) ((bFG1[v])^2) cFG1[v]-288 (E^(bFG0[v]+2 cFG0[v])) (v^2) bFG2[v] cFG1[v]+2688 (E^((5 cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+1944 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+1536 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+1176 (E^(3 cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]-288 (E^(3 cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]-1152 (E^((5 cFG0[v])/2)) (v^3) ((cFG1[v])^2)-972 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] ((cFG1[v])^2)-768 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)-1176 (E^(3 cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)+456 (E^(3 cFG0[v])) (v^2) ((cFG1[v])^3)+432 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] cFG2[v]+192 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cFG2[v]+672 (E^(3 cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]-864 (E^(3 cFG0[v])) (v^2) cFG1[v] cFG2[v]-576 (E^(3 cFG0[v])) (v^2) dEF3[((E^((cFG0[v])/2))/v)]+576 (E^(3 cFG0[v])) (v^2) dFG3[v]-96 (E^((5 cFG0[v])/2)) (v^3) bEF1'[((E^((cFG0[v])/2))/v)]-54 (E^(2 aFG0[v]+((3 cFG0[v])/2))) v ((aFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]-192 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-48 (E^((7 cFG0[v])/2)) v ((bEF1[((E^((cFG0[v])/2))/v)])^2) bEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((7 cFG0[v])/2)) v bEF2[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(bFG0[v]+((5 cFG0[v])/2))) v ((bFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]+96 (E^(bFG0[v]+((5 cFG0[v])/2))) v bFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]-192 (E^(3 cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-168 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((7 cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-192 (E^((7 cFG0[v])/2)) v cEF2[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+192 (E^(3 cFG0[v])) (v^2) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+216 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((7 cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+192 (E^((7 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-192 (E^((7 cFG0[v])/2)) v ((cFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]+192 (E^((7 cFG0[v])/2)) v cFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(aFG0[v]+3 cFG0[v])) aFG1[v] ((bEF1'[((E^((cFG0[v])/2))/v)])^2)+144 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] bEF2'[((E^((cFG0[v])/2))/v)]+96 (E^((5 cFG0[v])/2)) (v^3) cEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(aFG0[v]+2 cFG0[v])) (v^2) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+54 (E^(2 aFG0[v]+((3 cFG0[v])/2))) v ((aFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+192 (E^(3 cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^((7 cFG0[v])/2)) v ((bEF1[((E^((cFG0[v])/2))/v)])^2) cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((7 cFG0[v])/2)) v bEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-48 (E^(bFG0[v]+((5 cFG0[v])/2))) v ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^(bFG0[v]+((5 cFG0[v])/2))) v bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+192 (E^(3 cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+168 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+96 (E^((7 cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+192 (E^((7 cFG0[v])/2)) v cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-192 (E^(3 cFG0[v])) (v^2) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-216 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-96 (E^((7 cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-192 (E^((7 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+192 (E^((7 cFG0[v])/2)) v ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-192 (E^((7 cFG0[v])/2)) v cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-24 (E^(aFG0[v]+3 cFG0[v])) aFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+48 (E^(aFG0[v]+3 cFG0[v])) aFG1[v] ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+3 (E^((3 cFG0[v])/2)) v ((AEF0[((E^((cFG0[v])/2))/v)])^3) (24 (v^4)+4 (E^((3 cFG0[v])/2)) v ((bEF1[((E^((cFG0[v])/2))/v)])^3)-36 (E^((3 cFG0[v])/2)) v bEF3[((E^((cFG0[v])/2))/v)]-12 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)+4 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^3)-24 (E^(bFG0[v])) (v^2) bFG2[v]+24 (E^(bFG0[v]+((cFG0[v])/2))) v bFG1[v] bFG2[v]+24 (E^(bFG0[v]+((cFG0[v])/2))) v bFG3[v]+12 (E^((3 cFG0[v])/2)) v bFG3[v]+68 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]-10 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]-20 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]+64 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)+19 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^3)-20 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-60 (E^((cFG0[v])/2)) (v^3) cFG1[v]+6 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cFG1[v]+12 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cFG1[v]-112 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-49 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]+12 (E^((3 cFG0[v])/2)) v cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]+48 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)+49 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)-19 (E^((3 cFG0[v])/2)) v ((cFG1[v])^3)-28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]+36 (E^((3 cFG0[v])/2)) v cFG1[v] cFG2[v]+24 (E^((3 cFG0[v])/2)) v dEF3[((E^((cFG0[v])/2))/v)]-24 (E^((3 cFG0[v])/2)) v dFG3[v]+4 (E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)]-2 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(bFG0[v]+cFG0[v])) bFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-8 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) ((cFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) cFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(bFG0[v]+cFG0[v])) bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(cFG0[v])) ((bEF1[((E^((cFG0[v])/2))/v)])^2) (10 (v^2)+13 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-11 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+4 (E^(cFG0[v])) bEF2[((E^((cFG0[v])/2))/v)] (-6 (v^2)+5 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-3 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+4 (E^((cFG0[v])/2)) bEF1[((E^((cFG0[v])/2))/v)] (10 (v^3)-2 (E^(cFG0[v])) v bEF2[((E^((cFG0[v])/2))/v)]-2 (E^(bFG0[v])) v ((bFG1[v])^2)-4 (E^(bFG0[v])) v bFG2[v]+24 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+8 (E^(cFG0[v])) v ((cEF1[((E^((cFG0[v])/2))/v)])^2)+2 (E^(cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)]-20 (E^((cFG0[v])/2)) (v^2) cFG1[v]-16 (E^(cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+8 (E^(cFG0[v])) v ((cFG1[v])^2)-2 (E^(cFG0[v])) v cFG2[v]+2 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-2 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]))-144 (E^(aFG0[v]+((5 cFG0[v])/2))) v aFG1[v] cEF2'[((E^((cFG0[v])/2))/v)]+2 (E^((3 cFG0[v])/2)) v ((AEF0[((E^((cFG0[v])/2))/v)])^(5/2)) (108 (v^4)+38 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+12 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-18 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-36 (E^(bFG0[v])) (v^2) bFG2[v]+204 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+89 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-12 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-180 (E^((cFG0[v])/2)) (v^3) cFG1[v]-162 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+81 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-36 (E^(cFG0[v])) (v^2) cFG2[v]+14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-12 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-12 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+18 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+12 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)])+432 (E^((3 cFG0[v])/2)) (v^6) cFG0'[v]+648 (E^(aFG0[v]+cFG0[v])) (v^5) aFG1[v] cFG0'[v]+243 (E^(2 aFG0[v]+((cFG0[v])/2))) (v^4) ((aFG1[v])^2) cFG0'[v]+576 (E^(2 cFG0[v])) (v^5) bEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+384 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^4) aFG1[v] bEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+152 (E^((5 cFG0[v])/2)) (v^4) ((bEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+48 (E^((5 cFG0[v])/2)) (v^4) bEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]-72 (E^(bFG0[v]+((3 cFG0[v])/2))) (v^4) ((bFG1[v])^2) cFG0'[v]-144 (E^(bFG0[v]+((3 cFG0[v])/2))) (v^4) bFG2[v] cFG0'[v]+816 (E^(2 cFG0[v])) (v^5) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+588 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^4) aFG1[v] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+464 (E^((5 cFG0[v])/2)) (v^4) bEF1[((E^((cFG0[v])/2))/v)] cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+356 (E^((5 cFG0[v])/2)) (v^4) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-48 (E^((5 cFG0[v])/2)) (v^4) cEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]-720 (E^(2 cFG0[v])) (v^5) cFG1[v] cFG0'[v]-540 (E^(aFG0[v]+((3 cFG0[v])/2))) (v^4) aFG1[v] cFG1[v] cFG0'[v]-432 (E^((5 cFG0[v])/2)) (v^4) bEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]-648 (E^((5 cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]+324 (E^((5 cFG0[v])/2)) (v^4) ((cFG1[v])^2) cFG0'[v]-144 (E^((5 cFG0[v])/2)) (v^4) cFG2[v] cFG0'[v]+36 (E^(aFG0[v]+2 cFG0[v])) (v^3) aFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+16 (E^(3 cFG0[v])) (v^3) bEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+56 (E^(3 cFG0[v])) (v^3) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-72 (E^(3 cFG0[v])) (v^3) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^((7 cFG0[v])/2)) (v^2) ((bEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-48 (E^(3 cFG0[v])) (v^3) bEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]-48 (E^((5 cFG0[v])/2)) (v^4) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-36 (E^(aFG0[v]+2 cFG0[v])) (v^3) aFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-16 (E^(3 cFG0[v])) (v^3) bEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-56 (E^(3 cFG0[v])) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+72 (E^(3 cFG0[v])) (v^3) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^((7 cFG0[v])/2)) (v^2) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-16 (E^((7 cFG0[v])/2)) (v^2) ((cEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+48 (E^(3 cFG0[v])) (v^3) cEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]-108 (E^((3 cFG0[v])/2)) (v^7) ((cFG0'[v])^2)-81 (E^(aFG0[v]+cFG0[v])) (v^6) aFG1[v] ((cFG0'[v])^2)-64 (E^(2 cFG0[v])) (v^6) bEF1[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)-98 (E^(2 cFG0[v])) (v^6) cEF1[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)+90 (E^(2 cFG0[v])) (v^6) cFG1[v] ((cFG0'[v])^2)-6 (E^((5 cFG0[v])/2)) (v^5) bEF1'[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)+6 (E^((5 cFG0[v])/2)) (v^5) cEF1'[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)+9 (E^((3 cFG0[v])/2)) (v^8) ((cFG0'[v])^3)+18 (E^(2 (aFG0[v]+cFG0[v]))) ((aFG1[v])^2) bEF1''[((E^((cFG0[v])/2))/v)]-12 (E^(aFG0[v]+((5 cFG0[v])/2))) (v^2) aFG1[v] cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]+2 (E^(3 cFG0[v])) (v^4) ((cFG0'[v])^2) bEF1''[((E^((cFG0[v])/2))/v)]-18 (E^(2 (aFG0[v]+cFG0[v]))) ((aFG1[v])^2) cEF1''[((E^((cFG0[v])/2))/v)]+12 (E^(aFG0[v]+((5 cFG0[v])/2))) (v^2) aFG1[v] cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]-2 (E^(3 cFG0[v])) (v^4) ((cFG0'[v])^2) cEF1''[((E^((cFG0[v])/2))/v)]+9 (E^(2 cFG0[v])) ((AEF1[((E^((cFG0[v])/2))/v)])^2) (-81 (E^(aFG0[v])) (v^2) aFG1[v]-64 (E^(cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)]+(E^((cFG0[v])/2)) (-108 (v^3)-98 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+90 (E^((cFG0[v])/2)) (v^2) cFG1[v]-6 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+27 (v^4) cFG0'[v]+2 (E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-2 (E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)]))+(E^(cFG0[v])) ((AEF0[((E^((cFG0[v])/2))/v)])^2) (3 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (108 (v^4)+38 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+12 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-18 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-36 (E^(bFG0[v])) (v^2) bFG2[v]+204 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+89 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-12 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-180 (E^((cFG0[v])/2)) (v^3) cFG1[v]-162 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+81 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-36 (E^(cFG0[v])) (v^2) cFG2[v]+14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-12 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-12 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+18 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+12 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)])-3 (E^(aFG0[v])) aFG1[v] (108 (v^4)+38 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+12 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-18 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-36 (E^(bFG0[v])) (v^2) bFG2[v]+204 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+89 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-12 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-180 (E^((cFG0[v])/2)) (v^3) cFG1[v]-162 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+81 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-36 (E^(cFG0[v])) (v^2) cFG2[v]+14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-12 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-12 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-14 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+18 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+2 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-4 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+4 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)])+12 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)])+(E^((cFG0[v])/2)) v (-216 (v^4)-72 (E^((3 cFG0[v])/2)) v ((bEF1[((E^((cFG0[v])/2))/v)])^3)+648 (E^((3 cFG0[v])/2)) v bEF3[((E^((cFG0[v])/2))/v)]+216 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-72 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^3)+432 (E^(bFG0[v])) (v^2) bFG2[v]-432 (E^(bFG0[v]+((cFG0[v])/2))) v bFG1[v] bFG2[v]-432 (E^(bFG0[v]+((cFG0[v])/2))) v bFG3[v]-216 (E^((3 cFG0[v])/2)) v bFG3[v]-1028 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+180 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]+360 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]-1152 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-342 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^3)+360 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]+900 (E^((cFG0[v])/2)) (v^3) cFG1[v]-108 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cFG1[v]-216 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cFG1[v]+2016 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+882 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]-216 (E^((3 cFG0[v])/2)) v cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]-864 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-882 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)+342 (E^((3 cFG0[v])/2)) v ((cFG1[v])^3)+504 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]-648 (E^((3 cFG0[v])/2)) v cFG1[v] cFG2[v]-432 (E^((3 cFG0[v])/2)) v dEF3[((E^((cFG0[v])/2))/v)]+432 (E^((3 cFG0[v])/2)) v dFG3[v]-60 (E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)]+36 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]+72 (E^(bFG0[v]+cFG0[v])) bFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]-144 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-144 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+144 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-144 (E^(2 cFG0[v])) ((cFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(2 cFG0[v])) cFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]+60 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-36 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-72 (E^(bFG0[v]+cFG0[v])) bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+144 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-144 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-144 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(2 cFG0[v])) ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]-144 (E^(2 cFG0[v])) cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]+108 (v^5) cFG0'[v]-18 (E^(bFG0[v])) (v^3) ((bFG1[v])^2) cFG0'[v]-36 (E^(bFG0[v])) (v^3) bFG2[v] cFG0'[v]+204 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+89 (E^(cFG0[v])) (v^3) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-12 (E^(cFG0[v])) (v^3) cEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]-180 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-162 (E^(cFG0[v])) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]+81 (E^(cFG0[v])) (v^3) ((cFG1[v])^2) cFG0'[v]-36 (E^(cFG0[v])) (v^3) cFG2[v] cFG0'[v]+14 (E^((3 cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-18 (E^((3 cFG0[v])/2)) (v^2) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+2 (E^(2 cFG0[v])) v ((bEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-12 (E^((3 cFG0[v])/2)) (v^2) bEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]-12 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-14 (E^((3 cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+18 (E^((3 cFG0[v])/2)) (v^2) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+2 (E^(2 cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-4 (E^(2 cFG0[v])) v ((cEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+12 (E^((3 cFG0[v])/2)) (v^2) cEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]-2 (E^(cFG0[v])) ((bEF1[((E^((cFG0[v])/2))/v)])^2) (180 (v^2)+234 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-198 (E^((cFG0[v])/2)) v cFG1[v]+18 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-19 (v^3) cFG0'[v])-12 (E^(cFG0[v])) bEF2[((E^((cFG0[v])/2))/v)] (-36 (v^2)+30 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-18 (E^((cFG0[v])/2)) v cFG1[v]+6 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-6 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-(v^3) cFG0'[v])-4 (E^((cFG0[v])/2)) bEF1[((E^((cFG0[v])/2))/v)] (148 (v^3)-36 (E^(cFG0[v])) v bEF2[((E^((cFG0[v])/2))/v)]-36 (E^(bFG0[v])) v ((bFG1[v])^2)-72 (E^(bFG0[v])) v bFG2[v]+432 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+144 (E^(cFG0[v])) v ((cEF1[((E^((cFG0[v])/2))/v)])^2)+36 (E^(cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)]-360 (E^((cFG0[v])/2)) (v^2) cFG1[v]-288 (E^(cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+144 (E^(cFG0[v])) v ((cFG1[v])^2)-36 (E^(cFG0[v])) v cFG2[v]+36 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+18 (E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^((3 cFG0[v])/2)) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-36 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-18 (E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+18 (E^((3 cFG0[v])/2)) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-36 (v^4) cFG0'[v]-29 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+27 (E^((cFG0[v])/2)) (v^3) cFG1[v] cFG0'[v]-(E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+(E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v])-4 (E^((3 cFG0[v])/2)) v bEF1''[((E^((cFG0[v])/2))/v)]+4 (E^((3 cFG0[v])/2)) v cEF1''[((E^((cFG0[v])/2))/v)]))+3 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (243 (E^(2 aFG0[v])) (v^2) ((aFG1[v])^2)-6 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] (-108 (v^3)-64 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]-98 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+90 (E^((cFG0[v])/2)) (v^2) cFG1[v]-6 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+27 (v^4) cFG0'[v]+2 (E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-2 (E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+(E^(cFG0[v])) (432 (v^4)+152 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+48 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-72 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-144 (E^(bFG0[v])) (v^2) bFG2[v]+816 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+356 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-48 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-720 (E^((cFG0[v])/2)) (v^3) cFG1[v]-648 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+324 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-144 (E^(cFG0[v])) (v^2) cFG2[v]+56 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-72 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-48 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-48 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-56 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+72 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-16 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+48 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)]-216 (v^5) cFG0'[v]-196 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+180 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-12 (E^(cFG0[v])) (v^3) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+12 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+27 (v^6) ((cFG0'[v])^2)+16 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-8 (v^3) cFG0'[v])+4 (E^((3 cFG0[v])/2)) (v^2) cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]-4 (E^((3 cFG0[v])/2)) (v^2) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]))-4 (E^(cFG0[v])) v ((AEF0[((E^((cFG0[v])/2))/v)])^(3/2)) (3 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (-54 (v^3)-32 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]-49 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+45 (E^((cFG0[v])/2)) (v^2) cFG1[v]-3 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+3 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+3 (E^(aFG0[v])) aFG1[v] (54 (v^3)+32 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]+49 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]-45 (E^((cFG0[v])/2)) (v^2) cFG1[v]+3 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]-3 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+(E^((cFG0[v])/2)) (198 (v^4)+76 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+24 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-36 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-72 (E^(bFG0[v])) (v^2) bFG2[v]+408 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+178 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-24 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-360 (E^((cFG0[v])/2)) (v^3) cFG1[v]-324 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+162 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-72 (E^(cFG0[v])) (v^2) cFG2[v]+28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-36 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-24 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+36 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+24 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)]-54 (v^5) cFG0'[v]-49 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+45 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-3 (E^(cFG0[v])) (v^3) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+3 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-4 (v^3) cFG0'[v])+(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]))+2 (E^((cFG0[v])/2)) v (Sqrt[AEF0[((E^((cFG0[v])/2))/v)]]) (243 (E^(2 cFG0[v])) (v^2) ((AEF1[((E^((cFG0[v])/2))/v)])^2)+243 (E^(2 aFG0[v])) (v^2) ((aFG1[v])^2)-6 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] (-108 (v^3)-64 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]-98 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+90 (E^((cFG0[v])/2)) (v^2) cFG1[v]-6 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+27 (v^4) cFG0'[v]+2 (E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-2 (E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+(E^(cFG0[v])) (432 (v^4)+152 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+48 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-72 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-144 (E^(bFG0[v])) (v^2) bFG2[v]+816 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+356 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-48 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-720 (E^((cFG0[v])/2)) (v^3) cFG1[v]-648 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+324 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-144 (E^(cFG0[v])) (v^2) cFG2[v]+56 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-72 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-48 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-48 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-56 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+72 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+8 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-16 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+48 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)]-216 (v^5) cFG0'[v]-196 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+180 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-12 (E^(cFG0[v])) (v^3) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+12 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+27 (v^6) ((cFG0'[v])^2)+16 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-8 (v^3) cFG0'[v])+4 (E^((3 cFG0[v])/2)) (v^2) cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]-4 (E^((3 cFG0[v])/2)) (v^2) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)])+6 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (-81 (E^(aFG0[v])) (v^2) aFG1[v]-64 (E^(cFG0[v])) (v^2) bEF1[((E^((cFG0[v])/2))/v)]+(E^((cFG0[v])/2)) (-108 (v^3)-98 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+90 (E^((cFG0[v])/2)) (v^2) cFG1[v]-6 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+6 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+27 (v^4) cFG0'[v]+2 (E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-2 (E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])))+(E^((cFG0[v])/2)) AEF0[((E^((cFG0[v])/2))/v)] (-9 (E^(2 cFG0[v])) ((AEF1[((E^((cFG0[v])/2))/v)])^2) (-54 (v^3)-32 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]-49 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+45 (E^((cFG0[v])/2)) (v^2) cFG1[v]-3 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+3 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+9 (E^(2 aFG0[v])) ((aFG1[v])^2) (54 (v^3)+32 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]+49 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]-45 (E^((cFG0[v])/2)) (v^2) cFG1[v]+3 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]-3 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+6 (E^(aFG0[v]+((cFG0[v])/2))) aFG1[v] (162 (v^4)+76 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+24 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-36 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-72 (E^(bFG0[v])) (v^2) bFG2[v]+408 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+178 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-24 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-360 (E^((cFG0[v])/2)) (v^3) cFG1[v]-324 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+162 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-72 (E^(cFG0[v])) (v^2) cFG2[v]+28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-36 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-24 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+36 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+24 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)]-54 (v^5) cFG0'[v]-49 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+45 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-3 (E^(cFG0[v])) (v^3) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+3 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-4 (v^3) cFG0'[v])+(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)])+(E^(cFG0[v])) v (432 (v^4)+144 (E^((3 cFG0[v])/2)) v ((bEF1[((E^((cFG0[v])/2))/v)])^3)-1296 (E^((3 cFG0[v])/2)) v bEF3[((E^((cFG0[v])/2))/v)]-432 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)+144 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^3)-864 (E^(bFG0[v])) (v^2) bFG2[v]+864 (E^(bFG0[v]+((cFG0[v])/2))) v bFG1[v] bFG2[v]+864 (E^(bFG0[v]+((cFG0[v])/2))) v bFG3[v]+432 (E^((3 cFG0[v])/2)) v bFG3[v]+2056 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]-360 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cEF1[((E^((cFG0[v])/2))/v)]-720 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cEF1[((E^((cFG0[v])/2))/v)]+2304 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)+684 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^3)-720 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF2[((E^((cFG0[v])/2))/v)]-1800 (E^((cFG0[v])/2)) (v^3) cFG1[v]+216 (E^(bFG0[v]+((cFG0[v])/2))) v ((bFG1[v])^2) cFG1[v]+432 (E^(bFG0[v]+((cFG0[v])/2))) v bFG2[v] cFG1[v]-4032 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]-1764 (E^((3 cFG0[v])/2)) v ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG1[v]+432 (E^((3 cFG0[v])/2)) v cEF2[((E^((cFG0[v])/2))/v)] cFG1[v]+1728 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)+1764 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] ((cFG1[v])^2)-684 (E^((3 cFG0[v])/2)) v ((cFG1[v])^3)-1008 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cFG2[v]+1296 (E^((3 cFG0[v])/2)) v cFG1[v] cFG2[v]+864 (E^((3 cFG0[v])/2)) v dEF3[((E^((cFG0[v])/2))/v)]-864 (E^((3 cFG0[v])/2)) v dFG3[v]+120 (E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)]-72 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]-144 (E^(bFG0[v]+cFG0[v])) bFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]+288 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]+288 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-288 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-288 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+288 (E^(2 cFG0[v])) ((cFG1[v])^2) bEF1'[((E^((cFG0[v])/2))/v)]-288 (E^(2 cFG0[v])) cFG2[v] bEF1'[((E^((cFG0[v])/2))/v)]-120 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]+72 (E^(bFG0[v]+cFG0[v])) ((bFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+144 (E^(bFG0[v]+cFG0[v])) bFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-288 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-288 (E^(2 cFG0[v])) cEF2[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+288 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+288 (E^(2 cFG0[v])) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-288 (E^(2 cFG0[v])) ((cFG1[v])^2) cEF1'[((E^((cFG0[v])/2))/v)]+288 (E^(2 cFG0[v])) cFG2[v] cEF1'[((E^((cFG0[v])/2))/v)]-324 (v^5) cFG0'[v]+72 (E^(bFG0[v])) (v^3) ((bFG1[v])^2) cFG0'[v]+144 (E^(bFG0[v])) (v^3) bFG2[v] cFG0'[v]-816 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]-356 (E^(cFG0[v])) (v^3) ((cEF1[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+48 (E^(cFG0[v])) (v^3) cEF2[((E^((cFG0[v])/2))/v)] cFG0'[v]+720 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]+648 (E^(cFG0[v])) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v] cFG0'[v]-324 (E^(cFG0[v])) (v^3) ((cFG1[v])^2) cFG0'[v]+144 (E^(cFG0[v])) (v^3) cFG2[v] cFG0'[v]-56 (E^((3 cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+72 (E^((3 cFG0[v])/2)) (v^2) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-8 (E^(2 cFG0[v])) v ((bEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]+48 (E^((3 cFG0[v])/2)) (v^2) bEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]+48 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+56 (E^((3 cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-72 (E^((3 cFG0[v])/2)) (v^2) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]-8 (E^(2 cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+16 (E^(2 cFG0[v])) v ((cEF1'[((E^((cFG0[v])/2))/v)])^2) cFG0'[v]-48 (E^((3 cFG0[v])/2)) (v^2) cEF2'[((E^((cFG0[v])/2))/v)] cFG0'[v]+54 (v^6) ((cFG0'[v])^2)+49 (E^((cFG0[v])/2)) (v^5) cEF1[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)-45 (E^((cFG0[v])/2)) (v^5) cFG1[v] ((cFG0'[v])^2)+3 (E^(cFG0[v])) (v^4) bEF1'[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)-3 (E^(cFG0[v])) (v^4) cEF1'[((E^((cFG0[v])/2))/v)] ((cFG0'[v])^2)+8 (E^(cFG0[v])) ((bEF1[((E^((cFG0[v])/2))/v)])^2) (90 (v^2)+117 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-99 (E^((cFG0[v])/2)) v cFG1[v]+9 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-9 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-19 (v^3) cFG0'[v])+48 (E^(cFG0[v])) bEF2[((E^((cFG0[v])/2))/v)] (-18 (v^2)+15 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-9 (E^((cFG0[v])/2)) v cFG1[v]+3 (E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-3 (E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-(v^3) cFG0'[v])+16 (E^((cFG0[v])/2)) bEF1[((E^((cFG0[v])/2))/v)] (74 (v^3)-18 (E^(cFG0[v])) v bEF2[((E^((cFG0[v])/2))/v)]-18 (E^(bFG0[v])) v ((bFG1[v])^2)-36 (E^(bFG0[v])) v bFG2[v]+216 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]+72 (E^(cFG0[v])) v ((cEF1[((E^((cFG0[v])/2))/v)])^2)+18 (E^(cFG0[v])) v cEF2[((E^((cFG0[v])/2))/v)]-180 (E^((cFG0[v])/2)) (v^2) cFG1[v]-144 (E^(cFG0[v])) v cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+72 (E^(cFG0[v])) v ((cFG1[v])^2)-18 (E^(cFG0[v])) v cFG2[v]+18 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]+9 (E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-9 (E^((3 cFG0[v])/2)) cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]-18 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-9 (E^((3 cFG0[v])/2)) cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+9 (E^((3 cFG0[v])/2)) cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]-36 (v^4) cFG0'[v]-29 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+27 (E^((cFG0[v])/2)) (v^3) cFG1[v] cFG0'[v]-(E^(cFG0[v])) (v^2) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+(E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+2 (v^5) ((cFG0'[v])^2))+8 (E^((3 cFG0[v])/2)) v bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) (v^3) ((cFG0'[v])^2) bEF1''[((E^((cFG0[v])/2))/v)]-8 (E^((3 cFG0[v])/2)) v cEF1''[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) (v^3) ((cFG0'[v])^2) cEF1''[((E^((cFG0[v])/2))/v)])-6 (E^(cFG0[v])) AEF1[((E^((cFG0[v])/2))/v)] (3 (E^(aFG0[v])) aFG1[v] (54 (v^3)+32 (E^((cFG0[v])/2)) (v^2) bEF1[((E^((cFG0[v])/2))/v)]+49 (E^((cFG0[v])/2)) (v^2) cEF1[((E^((cFG0[v])/2))/v)]-45 (E^((cFG0[v])/2)) (v^2) cFG1[v]+3 (E^(cFG0[v])) v bEF1'[((E^((cFG0[v])/2))/v)]-3 (E^(cFG0[v])) v cEF1'[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) bEF1''[((E^((cFG0[v])/2))/v)]+(E^((3 cFG0[v])/2)) cEF1''[((E^((cFG0[v])/2))/v)])+(E^((cFG0[v])/2)) (162 (v^4)+76 (E^(cFG0[v])) (v^2) ((bEF1[((E^((cFG0[v])/2))/v)])^2)+24 (E^(cFG0[v])) (v^2) bEF2[((E^((cFG0[v])/2))/v)]-36 (E^(bFG0[v])) (v^2) ((bFG1[v])^2)-72 (E^(bFG0[v])) (v^2) bFG2[v]+408 (E^((cFG0[v])/2)) (v^3) cEF1[((E^((cFG0[v])/2))/v)]+178 (E^(cFG0[v])) (v^2) ((cEF1[((E^((cFG0[v])/2))/v)])^2)-24 (E^(cFG0[v])) (v^2) cEF2[((E^((cFG0[v])/2))/v)]-360 (E^((cFG0[v])/2)) (v^3) cFG1[v]-324 (E^(cFG0[v])) (v^2) cEF1[((E^((cFG0[v])/2))/v)] cFG1[v]+162 (E^(cFG0[v])) (v^2) ((cFG1[v])^2)-72 (E^(cFG0[v])) (v^2) cFG2[v]+28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] bEF1'[((E^((cFG0[v])/2))/v)]-36 (E^((3 cFG0[v])/2)) v cFG1[v] bEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) ((bEF1'[((E^((cFG0[v])/2))/v)])^2)-24 (E^((3 cFG0[v])/2)) v bEF2'[((E^((cFG0[v])/2))/v)]-24 (E^(cFG0[v])) (v^2) cEF1'[((E^((cFG0[v])/2))/v)]-28 (E^((3 cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]+36 (E^((3 cFG0[v])/2)) v cFG1[v] cEF1'[((E^((cFG0[v])/2))/v)]+4 (E^(2 cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)] cEF1'[((E^((cFG0[v])/2))/v)]-8 (E^(2 cFG0[v])) ((cEF1'[((E^((cFG0[v])/2))/v)])^2)+24 (E^((3 cFG0[v])/2)) v cEF2'[((E^((cFG0[v])/2))/v)]-54 (v^5) cFG0'[v]-49 (E^((cFG0[v])/2)) (v^4) cEF1[((E^((cFG0[v])/2))/v)] cFG0'[v]+45 (E^((cFG0[v])/2)) (v^4) cFG1[v] cFG0'[v]-3 (E^(cFG0[v])) (v^3) bEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+3 (E^(cFG0[v])) (v^3) cEF1'[((E^((cFG0[v])/2))/v)] cFG0'[v]+8 (E^((cFG0[v])/2)) v bEF1[((E^((cFG0[v])/2))/v)] (36 (v^2)+29 (E^((cFG0[v])/2)) v cEF1[((E^((cFG0[v])/2))/v)]-27 (E^((cFG0[v])/2)) v cFG1[v]+(E^(cFG0[v])) bEF1'[((E^((cFG0[v])/2))/v)]-(E^(cFG0[v])) cEF1'[((E^((cFG0[v])/2))/v)]-4 (v^3) cFG0'[v])+(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] bEF1''[((E^((cFG0[v])/2))/v)]-(E^((3 cFG0[v])/2)) (v^2) cFG0'[v] cEF1''[((E^((cFG0[v])/2))/v)]))));

checko31=Expand[checko3[[1]]];

checko32=Expand[checko3[[2]]];

testo3=Expand[SeriesCoefficient[Series[dτdτ+(1/(v^2))Exp[aFG0[v]+u aFG1[v]+(u^2)aFG2[v]+(u^3)aFG3[v]],{u,0,3}]//.Union[subsTRAFO,subsAEF0],3]];

If these expressions are zero, the coordinate transformation works also in this order. Because the formulas are very long, the answer is provided in power series expansion at the boundary. Its accuraccy might be increased on faster machines.

Procedures

xxx[ch_Integer]:=FactorInteger[ch]/.{List[ah_Integer,bh_Integer]->bh Log[ah],List->Plus}

subsFLOOR={Floor[((π+2 Arg[v]-Arg[3+(v^4)])/(2 π))]->0,Floor[((π+Arg[v]-Arg[I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-I (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v-I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-2 (Sqrt[3]) v+I (Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1-I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[(-1+I) (2 (Sqrt[3]) v+(Sqrt[2]) (3^(1/4)) (Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((π+Arg[v]-Arg[-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[(Sqrt[3])-(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((π+Arg[v]-(1/2) Arg[3+(v^4)])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1-I) ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[(1+I) ((Sqrt[3])-(Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[(1+I) ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])-(Sqrt[3+(v^4)]))])/(2 π))]->-1,Floor[((Arg[-I ((Sqrt[3])-I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->0,Floor[((Arg[-(Sqrt[3])+(Sqrt[3+(v^4)])])/(2 π))]->0,Floor[((Arg[I ((Sqrt[3])+I (Sqrt[2]) (3^(1/4)) v-(Sqrt[3+(v^4)]))])/(2 π))]->-1};

subsCOMBO={Log[ah_Integer]->xxx[ah],Log[ah_Complex]->Log[Abs[ah]]+I Arg[ah],(E^(2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)+I 2Sin[ah]Cos[ah],(E^(-2 I ah_))->((Cos[ah])^2)-((Sin[ah])^2)-I 2Sin[ah]Cos[ah],Log[Times[ah_,bh_]]->Log[ah]+Log[bh],Log[Times[ah_,bh_,ch_]]->Log[ah]+Log[bh]+Log[ch],Log[(1/(ah_))]->-Log[ah],

Log[v-(I/w)]->Log[v w-I]-Log[w],Log[v+(I/w)]->Log[v w+I]-Log[w],Log[v w-I]->Log[1+(v^2)(w^2)]-Log[I+v w],Log[1-((1/2)-(I/2)) (1+v w)]->Log[1+(v^2)(w^2)]-Log[1-((1/2)+(I/2)) (1+v w)]-Log[2],Log[1+I v w]->Log[I]+Log[-I+v w],Log[1-I v w]->Log[-I]+Log[I+v w],Log[1-((1/2)+(I/2)) (v-(I/w)) w]->2Log[-1+v w]-Log[2]-Log[1-((1/2)-(I/2)) (v+(I/w)) w],
Log[((v w)/(Sqrt[1+(v^2) (w^2)]))]->Log[v]+Log[w]-(1/2)Log[1+(v^2)(w^2)],Log[-1+(v^4) (w^4)]->Log[-1+v w]+Log[1+v w]+Log[1+(v^2)(w^2)],Log[1+(1/2) I (v+(I/w)) w]->Log[1+(v^2)(w^2)]-Log[4]-Log[1-(1/2) I (v-(I/w)) w],Log[1-v w]->I π+Log[-1+v w],Log[(1+I)-(1-I) v w]->Log[2]+Log[1+(v^2)(w^2)]-Log[(1-I)-(1+I) v w],ArcTan[((1+v w)/(1-v w))]->ArcTan[((-1+v w)/(1+v w))]-(π/2),ArcTan[((1+v w)/(-1+v w))]->-ArcTan[((-1+v w)/(1+v w))]+(π/2),ArcTan[((1-v w)/(1+v w))]->-ArcTan[((-1+v w)/(1+v w))],
Log[(1-I)-(1+I)v w]->Log[1+I]+Log[I+v w]-I π,Log[((1/2)+(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[-1+v w],Log[((1/2)-(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-1+v w],Log[v-(1/w)]->Log[-1+v w]-Log[w],Log[((1/2)-(I/2))-((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]-I π+Log[I+v w],Log[((1/2)+(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[1+v w],Log[((1/2)+(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[I+v w],Log[((1/2)-(I/2))+((1/2)+(I/2)) v w]->Log[(1/2)+(I/2)]+Log[-I+v w],Log[((1/2)+(I/2))-((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+I π+Log[-I+v w],Log[((1/2)-(I/2))+((1/2)-(I/2)) v w]->Log[(1/2)-(I/2)]+Log[1+v w],Log[1-(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))+(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[v]+Log[w]-Log[I+v w],Log[1-I ((1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2))))]->Log[1+I]+Log[1+v w]-Log[I+v w],Log[1+(1/(1+(v^2) (w^2)))-((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+Log[I]-I π-Log[-I+v w],Log[v+(1/w)]->Log[1+v w]-Log[w],Log[1-(1/2) I (v-(I/w)) w]->-Log[2]+Log[I+v w]-I (π/2),Log[1+((1/2)+(I/2)) (I+v w)]->Log[(1/2)+(I/2)]+Log[1+v w],Log[1-((1/2)+(I/2)) (1+v w)]->Log[(1/2)+(I/2)]+Log[I+v w]-I π,Log[1+(1/(1+(v^2) (w^2)))+((2 I v w)/(1+(v^2) (w^2)))-(((v^2) (w^2))/(1+(v^2) (w^2)))]->Log[2]+I (π/2)-Log[I+v w],Log[(((1+v w))^2)]->2Log[1+v w], Log[-1+(v^2) (w^2)]->Log[-1+v w]+Log[1+v w]};

bEF2v[v_]=(1/(9 (v^3) (-2+(Sqrt[2]) (3^(1/4)) v) (((2+(Sqrt[2]) (3^(1/4)) v))^2) (((2+(Sqrt[3]) (v^2)))^2)))2 (256-64 D1a-32 (D1a^2)+80 (Sqrt[2]) (3^(1/4)) v-64 (Sqrt[2]) (3^(1/4)) D1a v-16 (Sqrt[2]) (3^(1/4)) (D1a^2) v-96 D2a v+136 (Sqrt[3]) (v^2)-64 (Sqrt[3]) D1a (v^2)-16 (Sqrt[3]) (D1a^2) (v^2)-48 (Sqrt[2]) (3^(1/4)) D2a (v^2)-16 (Sqrt[3]) π (v^2)+68 (Sqrt[2]) (3^(3/4)) (v^3)-32 (Sqrt[2]) (3^(3/4)) D1a (v^3)-8 (Sqrt[2]) (3^(3/4)) (D1a^2) (v^3)-48 (Sqrt[3]) D2a (v^3)-8 (Sqrt[2]) (3^(3/4)) π (v^3)-312 (v^4)-96 D1a (v^4)+24 (D1a^2) (v^4)-24 (Sqrt[2]) (3^(3/4)) D2a (v^4)-24 π (v^4)-72 (Sqrt[2]) (3^(1/4)) (v^5)+72 (Sqrt[2]) (3^(1/4)) D1a (v^5)+12 (Sqrt[2]) (3^(1/4)) (D1a^2) (v^5)+72 D2a (v^5)-66 (Sqrt[3]) (v^6)+72 (Sqrt[3]) D1a (v^6)+12 (Sqrt[3]) (D1a^2) (v^6)+36 (Sqrt[2]) (3^(1/4)) D2a (v^6)+12 (Sqrt[3]) π (v^6)-33 (Sqrt[2]) (3^(3/4)) (v^7)+36 (Sqrt[2]) (3^(3/4)) D1a (v^7)+6 (Sqrt[2]) (3^(3/4)) (D1a^2) (v^7)+36 (Sqrt[3]) D2a (v^7)+6 (Sqrt[2]) (3^(3/4)) π (v^7)+18 (Sqrt[2]) (3^(3/4)) D2a (v^8)+18 π (v^8)-v (6 (Sqrt[2]) (3^(1/4))+14 (Sqrt[3]) v+7 (Sqrt[2]) (3^(3/4)) (v^2)+21 (v^3)) (-4+3 (v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+12 (Sqrt[2]) (3^(1/4)) (v^5) Log[(4/3)]+12 (Sqrt[3]) (v^6) Log[(4/3)]+6 (Sqrt[2]) (3^(3/4)) (v^7) Log[(4/3)]+18 (v^8) Log[(4/3)]-8 (Sqrt[3]) (v^2) Log[16]-4 (Sqrt[2]) (3^(3/4)) (v^3) Log[16]-12 (v^4) Log[16]-6 (Sqrt[2]) (3^(1/4)) (v^5) Log[16]-24 (v^5) (2 (Sqrt[2]) (3^(1/4))+2 (Sqrt[3]) v+(Sqrt[2]) (3^(3/4)) (v^2)+3 (v^3)) Log[v]-32 (Sqrt[3]) (v^2) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]-16 (Sqrt[2]) (3^(3/4)) (v^3) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]-48 (v^4) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+24 (Sqrt[3]) (v^6) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+12 (Sqrt[2]) (3^(3/4)) (v^7) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+36 (v^8) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+16 (Sqrt[3]) (v^2) Log[1+(((Sqrt[3]) (v^2))/2)]+8 (Sqrt[2]) (3^(3/4)) (v^3) Log[1+(((Sqrt[3]) (v^2))/2)]+24 (v^4) Log[1+(((Sqrt[3]) (v^2))/2)]+24 (Sqrt[2]) (3^(1/4)) (v^5) Log[1+(((Sqrt[3]) (v^2))/2)]+12 (Sqrt[3]) (v^6) Log[1+(((Sqrt[3]) (v^2))/2)]+6 (Sqrt[2]) (3^(3/4)) (v^7) Log[1+(((Sqrt[3]) (v^2))/2)]+18 (v^8) Log[1+(((Sqrt[3]) (v^2))/2)]);

subsSOLo012wDERupto4={AEF0[v_]->1-(4/(3 (v^4))),AEF1[v_]->((8+8 D1a+4 (Sqrt[2]) (3^(1/4)) v+6 D1a (v^4))/(9 (v^5))),AEF2[v_]->(1/(54 (v^6)))(3 (Sqrt[2]) (3^(1/4)) v (4+3 (v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+2 (-12-24 D1a-12 (D1a^2)-12 (Sqrt[2]) (3^(1/4)) v-8 (Sqrt[2]) (3^(1/4)) D1a v-24 D2a v-3 (Sqrt[3]) (v^2)+9 (v^4)+18 D1a (v^4)+3 (D1a^2) (v^4)-18 D2a (v^5)+3 (Sqrt[3]) (v^2) Log[(4/3)]-(Sqrt[3]) (v^2) Log[4]-12 (Sqrt[3]) (v^2) Log[v]+6 (Sqrt[3]) (v^2) Log[1+(((Sqrt[3]) (v^2))/2)])),bEF1[v_]->((-8+4 D1a+(Sqrt[2]) (3^(1/4)) π v-2 (Sqrt[2]) (3^(1/4)) v ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+(Sqrt[2]) (3^(1/4)) v Log[(4/3)]-4 (Sqrt[2]) (3^(1/4)) v Log[v]+2 (Sqrt[2]) (3^(1/4)) v Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+(Sqrt[2]) (3^(1/4)) v Log[1+(((Sqrt[3]) (v^2))/2)])/(6 v)),cEF1[v_]->-((-8-8 D1a+(Sqrt[2]) (3^(1/4)) π v-2 (Sqrt[2]) (3^(1/4)) v ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+(Sqrt[2]) (3^(1/4)) v Log[(4/3)]-4 (Sqrt[2]) (3^(1/4)) v Log[v]+2 (Sqrt[2]) (3^(1/4)) v Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+(Sqrt[2]) (3^(1/4)) v Log[1+(((Sqrt[3]) (v^2))/2)])/(12 v)),dEF2[v_]->((8-8 D1a-4 (D1a^2)-4 (Sqrt[2]) (3^(1/4)) v-24 D2a v+(Sqrt[3]) π (v^2)-2 (3^(1/4)) v (-3 (Sqrt[2])+(3^(1/4)) v) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+(Sqrt[3]) (v^2) Log[(16/9)]-8 (Sqrt[3]) (v^2) Log[v]+2 (Sqrt[3]) (v^2) Log[1+(((3^(1/4)) v)/(Sqrt[2]))]+3 (Sqrt[3]) (v^2) Log[1+(((Sqrt[3]) (v^2))/2)])/(24 (v^2))),AEF0'[v_]->(16/(3 (v^5))),AEF1'[v_]->-((2 (20+8 (Sqrt[2]) (3^(1/4)) v+D1a (20+3 (v^4))))/(9 (v^6))),AEF2'[v_]->(1/(54 (v^7)))(-3 (Sqrt[2]) (3^(1/4)) v (20+3 (v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+2 (72+144 D1a+72 (D1a^2)+60 (Sqrt[2]) (3^(1/4)) v+40 (Sqrt[2]) (3^(1/4)) D1a v+120 D2a v+6 (Sqrt[3]) (v^2)-9 (v^4)-36 D1a (v^4)-6 (D1a^2) (v^4)+18 D2a (v^5)-12 (Sqrt[3]) (v^2) Log[(4/3)]+8 (Sqrt[3]) (v^2) Log[2]+48 (Sqrt[3]) (v^2) Log[v]-24 (Sqrt[3]) (v^2) Log[1+(((Sqrt[3]) (v^2))/2)])),bEF1'[v_]->((2 (-D1a+(8/((2+(Sqrt[2]) (3^(1/4)) v) (2+(Sqrt[3]) (v^2))))))/(3 (v^2))),cEF1'[v_]->((2 (-D1a-(4/((2+(Sqrt[2]) (3^(1/4)) v) (2+(Sqrt[3]) (v^2))))))/(3 (v^2))),dEF2'[v_]->(1/(6 (v^3) (2+(Sqrt[2]) (3^(1/4)) v) (2+(Sqrt[3]) (v^2))))(-16-4 (Sqrt[2]) (3^(1/4)) v+24 D2a v-6 (Sqrt[3]) (v^2)+12 (Sqrt[2]) (3^(1/4)) D2a (v^2)-3 (Sqrt[2]) (3^(3/4)) (v^3)+12 (Sqrt[3]) D2a (v^3)+6 (Sqrt[2]) (3^(3/4)) D2a (v^4)+4 D1a (2+(Sqrt[2]) (3^(1/4)) v) (2+(Sqrt[3]) (v^2))+2 (D1a^2) (2+(Sqrt[2]) (3^(1/4)) v) (2+(Sqrt[3]) (v^2))-3 v (2 (Sqrt[2]) (3^(1/4))+2 (Sqrt[3]) v+(Sqrt[2]) (3^(3/4)) (v^2)+3 (v^3)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]),AEF0''[v_]->-(80/(3 (v^6))),AEF1''[v_]->((4 (20 (3+(Sqrt[2]) (3^(1/4)) v)+3 D1a (20+(v^4))))/(9 (v^7))),AEF2''[v_]->(1/(27 (v^8) (2+(Sqrt[3]) (v^2))))(9 (Sqrt[2]) (3^(1/4)) v (2+(Sqrt[3]) (v^2)) (20+(v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+2 (-504-1008 D1a-504 (D1a^2)-360 (Sqrt[2]) (3^(1/4)) v-240 (Sqrt[2]) (3^(1/4)) D1a v-720 D2a v-264 (Sqrt[3]) (v^2)-504 (Sqrt[3]) D1a (v^2)-252 (Sqrt[3]) (D1a^2) (v^2)-180 (Sqrt[2]) (3^(3/4)) (v^3)-120 (Sqrt[2]) (3^(3/4)) D1a (v^3)-360 (Sqrt[3]) D2a (v^3)-18 (v^4)+108 D1a (v^4)+18 (D1a^2) (v^4)-36 D2a (v^5)+9 (Sqrt[3]) (v^6)+54 (Sqrt[3]) D1a (v^6)+9 (Sqrt[3]) (D1a^2) (v^6)-18 (Sqrt[3]) D2a (v^7)+60 (Sqrt[3]) (v^2) Log[(4/3)]+90 (v^4) Log[(4/3)]-40 (Sqrt[3]) (v^2) Log[2]-60 (v^4) Log[2]-120 (2 (Sqrt[3]) (v^2)+3 (v^4)) Log[v]+60 (2 (Sqrt[3]) (v^2)+3 (v^4)) Log[1+(((Sqrt[3]) (v^2))/2)])),bEF1''[v_]->((8 (-2 (8+6 (Sqrt[2]) (3^(1/4)) v+8 (Sqrt[3]) (v^2)+5 (Sqrt[2]) (3^(3/4)) (v^3))+D1a (8+8 (Sqrt[2]) (3^(1/4)) v+12 (Sqrt[3]) (v^2)+8 (Sqrt[2]) (3^(3/4)) (v^3)+18 (v^4)+6 (Sqrt[2]) (3^(1/4)) (v^5)+3 (Sqrt[3]) (v^6))))/(3 (v^3) (((2+(Sqrt[2]) (3^(1/4)) v))^2) (((2+(Sqrt[3]) (v^2)))^2))),cEF1''[v_]->((8 (8+6 (Sqrt[2]) (3^(1/4)) v+8 (Sqrt[3]) (v^2)+5 (Sqrt[2]) (3^(3/4)) (v^3)+D1a (8+8 (Sqrt[2]) (3^(1/4)) v+12 (Sqrt[3]) (v^2)+8 (Sqrt[2]) (3^(3/4)) (v^3)+18 (v^4)+6 (Sqrt[2]) (3^(1/4)) (v^5)+3 (Sqrt[3]) (v^6))))/(3 (v^3) (((2+(Sqrt[2]) (3^(1/4)) v))^2) (((2+(Sqrt[3]) (v^2)))^2))),dEF2''[v_]->((-2 (6 D1a+3 (D1a^2)+((2 (-48-8 (5 (Sqrt[2]) (3^(1/4))-6 D2a) v+(-52 (Sqrt[3])+48 (Sqrt[2]) (3^(1/4)) D2a) (v^2)-8 (4 (Sqrt[2]) (3^(3/4))-9 (Sqrt[3]) D2a) (v^3)+48 (-1+(Sqrt[2]) (3^(3/4)) D2a) (v^4)-18 ((Sqrt[2]) (3^(1/4))-6 D2a) (v^5)-9 ((Sqrt[3])-4 (Sqrt[2]) (3^(1/4)) D2a) (v^6)+18 (Sqrt[3]) D2a (v^7)))/((((2+(Sqrt[2]) (3^(1/4)) v))^2) (((2+(Sqrt[3]) (v^2)))^2))))+3 (Sqrt[2]) (3^(1/4)) v ArcTan[(((3^(1/4)) v)/(Sqrt[2]))])/(6 (v^4))),Derivative[3][AEF0][v_]->(160/(v^7)),Derivative[3][AEF1][v_]->-((4 (140+140 D1a+40 (Sqrt[2]) (3^(1/4)) v+3 D1a (v^4)))/(3 (v^8))),Derivative[3][AEF2][v_]->(1/(9 (v^9)))(-3 (Sqrt[2]) (3^(1/4)) v (140+3 (v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]+2 (1344 D1a+672 (D1a^2)+280 (Sqrt[2]) (3^(1/4)) D1a v+840 D2a v-72 D1a (v^4)-12 (D1a^2) (v^4)+18 D2a (v^5)+(2688/(((2+(Sqrt[3]) (v^2)))^2))+((1680 (Sqrt[2]) (3^(1/4)) v)/(((2+(Sqrt[3]) (v^2)))^2))+((2696 (Sqrt[3]) (v^2))/(((2+(Sqrt[3]) (v^2)))^2))+((1680 (Sqrt[2]) (3^(3/4)) (v^3))/(((2+(Sqrt[3]) (v^2)))^2))+((2100 (v^4))/(((2+(Sqrt[3]) (v^2)))^2))+((1260 (Sqrt[2]) (3^(1/4)) (v^5))/(((2+(Sqrt[3]) (v^2)))^2))+((30 (Sqrt[3]) (v^6))/(((2+(Sqrt[3]) (v^2)))^2))-((27 (v^8))/(((2+(Sqrt[3]) (v^2)))^2))-60 (Sqrt[3]) (v^2) Log[(4/3)]+40 (Sqrt[3]) (v^2) Log[2]+240 (Sqrt[3]) (v^2) Log[v]-120 (Sqrt[3]) (v^2) Log[1+(((Sqrt[3]) (v^2))/2)])),Derivative[3][bEF1][v_]->-(1/(3 (v^4) (((2+(Sqrt[2]) (3^(1/4)) v))^3) (((2+(Sqrt[3]) (v^2)))^3)))8 (-8 (24+32 (Sqrt[2]) (3^(1/4)) v+60 (Sqrt[3]) (v^2)+48 (Sqrt[2]) (3^(3/4)) (v^3)+162 (v^4)+72 (Sqrt[2]) (3^(1/4)) (v^5)+45 (Sqrt[3]) (v^6))+3 D1a (32+48 (Sqrt[2]) (3^(1/4)) v+96 (Sqrt[3]) (v^2)+80 (Sqrt[2]) (3^(3/4)) (v^3)+288 (v^4)+144 (Sqrt[2]) (3^(1/4)) (v^5)+120 (Sqrt[3]) (v^6)+36 (Sqrt[2]) (3^(3/4)) (v^7)+54 (v^8)+9 (Sqrt[2]) (3^(1/4)) (v^9))),Derivative[3][cEF1][v_]->-(1/(3 (v^4) (((2+(Sqrt[2]) (3^(1/4)) v))^3) (((2+(Sqrt[3]) (v^2)))^3)))8 (4 (24+32 (Sqrt[2]) (3^(1/4)) v+60 (Sqrt[3]) (v^2)+48 (Sqrt[2]) (3^(3/4)) (v^3)+162 (v^4)+72 (Sqrt[2]) (3^(1/4)) (v^5)+45 (Sqrt[3]) (v^6))+3 D1a (32+48 (Sqrt[2]) (3^(1/4)) v+96 (Sqrt[3]) (v^2)+80 (Sqrt[2]) (3^(3/4)) (v^3)+288 (v^4)+144 (Sqrt[2]) (3^(1/4)) (v^5)+120 (Sqrt[3]) (v^6)+36 (Sqrt[2]) (3^(3/4)) (v^7)+54 (v^8)+9 (Sqrt[2]) (3^(1/4)) (v^9))),Derivative[3][dEF2][v_]->(1/(6 (v^5)))(4 (12 D1a+6 (D1a^2)+(1/((((2+(Sqrt[2]) (3^(1/4)) v))^3) (((2+(Sqrt[3]) (v^2)))^3)))(-768-96 (11 (Sqrt[2]) (3^(1/4))-6 D2a) v+(-1936 (Sqrt[3])+864 (Sqrt[2]) (3^(1/4)) D2a) (v^2)-216 (7 (Sqrt[2]) (3^(3/4))-8 (Sqrt[3]) D2a) (v^3)+72 (-67+20 (Sqrt[2]) (3^(3/4)) D2a) (v^4)+(-2076 (Sqrt[2]) (3^(1/4))+5184 D2a) (v^5)-36 (41 (Sqrt[3])-72 (Sqrt[2]) (3^(1/4)) D2a) (v^6)+(-306 (Sqrt[2]) (3^(3/4))+2160 (Sqrt[3]) D2a) (v^7)+162 (-3+4 (Sqrt[2]) (3^(3/4)) D2a) (v^8)-81 ((Sqrt[2]) (3^(1/4))-12 D2a) (v^9)+162 (Sqrt[2]) (3^(1/4)) D2a (v^10)))-9 (Sqrt[2]) (3^(1/4)) v ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]),Derivative[4][AEF0][v_]->-(1120/(v^8)),Derivative[4][AEF1][v_]->((16 (70 (4+(Sqrt[2]) (3^(1/4)) v)+D1a (280+3 (v^4))))/(3 (v^9))),Derivative[4][AEF2][v_]->(4/9) (-(3024/(v^10))-((6048 D1a)/(v^10))-((3024 (D1a^2))/(v^10))-((1680 (Sqrt[2]) (3^(1/4)))/(v^9))-((1120 (Sqrt[2]) (3^(1/4)) D1a)/(v^9))-((3360 D2a)/(v^9))+((428 (Sqrt[3]))/(v^8))+(90/(v^6))+((180 D1a)/(v^6))+((30 (D1a^2))/(v^6))-((36 D2a)/(v^5))-((432 (Sqrt[3]))/(((2+(Sqrt[3]) (v^2)))^4))-(432/((v^2) (((2+(Sqrt[3]) (v^2)))^4)))-((324 (v^2))/(((2+(Sqrt[3]) (v^2)))^4))-((18 (Sqrt[3]))/(((2+(Sqrt[3]) (v^2)))^3))-((408 (Sqrt[3]))/((v^4) (((2+(Sqrt[3]) (v^2)))^3)))-(720/((v^2) (((2+(Sqrt[3]) (v^2)))^3)))-(960/((v^6) (((2+(Sqrt[3]) (v^2)))^2)))-((450 (Sqrt[3]))/((v^4) (((2+(Sqrt[3]) (v^2)))^2)))+(504/((v^2) (((2+(Sqrt[3]) (v^2)))^2)))-(135/(((v+(((Sqrt[3]) (v^3))/2)))^2))+(5670/(2 (Sqrt[3]) (v^4)+3 (v^6)))-((1908 (Sqrt[3]))/(2 (v^4)+(Sqrt[3]) (v^6)))-(1080/(2 (v^6)+(Sqrt[3]) (v^8)))-(2520/(2 (Sqrt[3]) (v^8)+3 (v^10)))+((3 (Sqrt[2]) (3^(1/4)) (280+3 (v^4)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))])/(v^9))+((210 (Sqrt[3]) Log[(4/3)])/(v^8))-((140 (Sqrt[3]) Log[2])/(v^8))-((840 (Sqrt[3]) Log[v])/(v^8))+((420 (Sqrt[3]) Log[1+(((Sqrt[3]) (v^2))/2)])/(v^8))),Derivative[4][bEF1][v_]->(1/((v^5) (((2+(Sqrt[2]) (3^(1/4)) v))^4) (((2+(Sqrt[3]) (v^2)))^4)))64 (-128-240 (Sqrt[2]) (3^(1/4)) v-576 (Sqrt[3]) (v^2)-560 (Sqrt[2]) (3^(3/4)) (v^3)-2496 (v^4)-1560 (Sqrt[2]) (3^(1/4)) (v^5)-1680 (Sqrt[3]) (v^6)-756 (Sqrt[2]) (3^(3/4)) (v^7)-1512 (v^8)-315 (Sqrt[2]) (3^(1/4)) (v^9)+D1a (64+128 (Sqrt[2]) (3^(1/4)) v+320 (Sqrt[3]) (v^2)+320 (Sqrt[2]) (3^(3/4)) (v^3)+1488 (v^4)+960 (Sqrt[2]) (3^(1/4)) (v^5)+1056 (Sqrt[3]) (v^6)+480 (Sqrt[2]) (3^(3/4)) (v^7)+1116 (v^8)+360 (Sqrt[2]) (3^(1/4)) (v^9)+180 (Sqrt[3]) (v^10)+36 (Sqrt[2]) (3^(3/4)) (v^11)+27 (v^12))),Derivative[4][cEF1][v_]->(1/((v^5) (((2+(Sqrt[2]) (3^(1/4)) v))^4) (((2+(Sqrt[3]) (v^2)))^4)))32 (128+240 (Sqrt[2]) (3^(1/4)) v+576 (Sqrt[3]) (v^2)+560 (Sqrt[2]) (3^(3/4)) (v^3)+2496 (v^4)+1560 (Sqrt[2]) (3^(1/4)) (v^5)+1680 (Sqrt[3]) (v^6)+756 (Sqrt[2]) (3^(3/4)) (v^7)+1512 (v^8)+315 (Sqrt[2]) (3^(1/4)) (v^9)+2 D1a (64+128 (Sqrt[2]) (3^(1/4)) v+320 (Sqrt[3]) (v^2)+320 (Sqrt[2]) (3^(3/4)) (v^3)+1488 (v^4)+960 (Sqrt[2]) (3^(1/4)) (v^5)+1056 (Sqrt[3]) (v^6)+480 (Sqrt[2]) (3^(3/4)) (v^7)+1116 (v^8)+360 (Sqrt[2]) (3^(1/4)) (v^9)+180 (Sqrt[3]) (v^10)+36 (Sqrt[2]) (3^(3/4)) (v^11)+27 (v^12))),Derivative[4][dEF2][v_]->-(1/((v^6) (((2+(Sqrt[2]) (3^(1/4)) v))^4) (((2+(Sqrt[3]) (v^2)))^4)))8 (2 (-640-64 (19 (Sqrt[2]) (3^(1/4))-6 D2a) v-192 (15 (Sqrt[3])-4 (Sqrt[2]) (3^(1/4)) D2a) (v^2)-64 (43 (Sqrt[2]) (3^(3/4))-30 (Sqrt[3]) D2a) (v^3)+48 (-251+40 (Sqrt[2]) (3^(3/4)) D2a) (v^4)+(-7248 (Sqrt[2]) (3^(1/4))+8928 D2a) (v^5)+(-7368 (Sqrt[3])+5760 (Sqrt[2]) (3^(1/4)) D2a) (v^6)-96 (31 (Sqrt[2]) (3^(3/4))-66 (Sqrt[3]) D2a) (v^7)+72 (-81+40 (Sqrt[2]) (3^(3/4)) D2a) (v^8)-216 (7 (Sqrt[2]) (3^(1/4))-31 D2a) (v^9)+(-522 (Sqrt[3])+2160 (Sqrt[2]) (3^(1/4)) D2a) (v^10)-108 ((Sqrt[2]) (3^(3/4))-10 (Sqrt[3]) D2a) (v^11)+27 (-3+8 (Sqrt[2]) (3^(3/4)) D2a) (v^12)+162 D2a (v^13)+10 D1a (64+128 (Sqrt[2]) (3^(1/4)) v+320 (Sqrt[3]) (v^2)+320 (Sqrt[2]) (3^(3/4)) (v^3)+1488 (v^4)+960 (Sqrt[2]) (3^(1/4)) (v^5)+1056 (Sqrt[3]) (v^6)+480 (Sqrt[2]) (3^(3/4)) (v^7)+1116 (v^8)+360 (Sqrt[2]) (3^(1/4)) (v^9)+180 (Sqrt[3]) (v^10)+36 (Sqrt[2]) (3^(3/4)) (v^11)+27 (v^12))+5 (D1a^2) (64+128 (Sqrt[2]) (3^(1/4)) v+320 (Sqrt[3]) (v^2)+320 (Sqrt[2]) (3^(3/4)) (v^3)+1488 (v^4)+960 (Sqrt[2]) (3^(1/4)) (v^5)+1056 (Sqrt[3]) (v^6)+480 (Sqrt[2]) (3^(3/4)) (v^7)+1116 (v^8)+360 (Sqrt[2]) (3^(1/4)) (v^9)+180 (Sqrt[3]) (v^10)+36 (Sqrt[2]) (3^(3/4)) (v^11)+27 (v^12)))-3 v (64 (Sqrt[2]) (3^(1/4))+256 (Sqrt[3]) v+320 (Sqrt[2]) (3^(3/4)) (v^2)+1920 (v^3)+1488 (Sqrt[2]) (3^(1/4)) (v^4)+1920 (Sqrt[3]) (v^5)+1056 (Sqrt[2]) (3^(3/4)) (v^6)+2880 (v^7)+1116 (Sqrt[2]) (3^(1/4)) (v^8)+720 (Sqrt[3]) (v^9)+180 (Sqrt[2]) (3^(3/4)) (v^10)+216 (v^11)+27 (Sqrt[2]) (3^(1/4)) (v^12)) ArcTan[(((3^(1/4)) v)/(Sqrt[2]))]),bEF2'[v_]->bEF2v[v],bEF2''[v_]->bEF2v'[v],bEF2'''[v_]->bEF2v''[v]};

cFG0[v_]=bFG0[v];

AEF3S[v_]=Normal[Simplify/@(Series[AEF3NEW[v],{v,∞,16}]//.Union[{Floor[((Arg[(1/(2 I+(Sqrt[2]) (3^(1/4)) v))])/(2 π))]->-1},subsCOMBO])]

bEF3S[v_]=Normal[Integrate[Simplify/@(Series[bEF3vNEW[v],{v,∞,16}]//.Union[{Floor[((Arg[(1/(2 I+(Sqrt[2]) (3^(1/4)) v))])/(2 π))]->-1},subsCOMBO]),v]]

dEF3S[v_]=Normal[Simplify/@(Series[dEF3NEW[v],{v,∞,16}]//.Union[{Floor[((Arg[(1/(2 I+(Sqrt[2]) (3^(1/4)) v))])/(2 π))]->-1},subsCOMBO])]

bEF2S[v_]=Normal[Integrate[Simplify/@(Series[bEF2v[v],{v,∞,16}]//.Union[{Floor[((Arg[(1/(2 I+(Sqrt[2]) (3^(1/4)) v))])/(2 π))]->-1},subsCOMBO]),v]]

Evaluation of testo3

testo3: Dividing into parts (3 order + bEF2[x]+rest)

testo3rest=testo3//.{AEF3[((E^((cFG0[v])/2))/v)]->0,AEF3'[((E^((cFG0[v])/2))/v)]->0,AEF3''[((E^((cFG0[v])/2))/v)]->0,bEF3[((E^((cFG0[v])/2))/v)]->0,bEF3'[((E^((cFG0[v])/2))/v)]->0,bEF3''[((E^((cFG0[v])/2))/v)]->0,dEF3[((E^((cFG0[v])/2))/v)]->0,dEF3'[((E^((cFG0[v])/2))/v)]->0,dEF3''[((E^((cFG0[v])/2))/v)]->0,bEF2[((E^((cFG0[v])/2))/v)]->0,aFG3[v]->0,AFG3'[v]->0,AFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0};

testo3bEF2=D[testo3,bEF2[((E^((cFG0[v])/2))/v)]]//Simplify

testo3AEF3=D[testo3,AEF3[((E^((cFG0[v])/2))/v)]]

testo3AEF3v=D[testo3,AEF3'[((E^((cFG0[v])/2))/v)]]

testo3AEF3vv=D[testo3,AEF3''[((E^((cFG0[v])/2))/v)]]

testo3bEF3=D[testo3,bEF3[((E^((cFG0[v])/2))/v)]]//Simplify

testo3bEF3v=D[testo3,bEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

testo3bEF3vv=D[testo3,bEF3''[((E^((cFG0[v])/2))/v)]]

testo3dEF3=D[testo3,dEF3[((E^((cFG0[v])/2))/v)]]//Simplify

testo3dEF3v=D[testo3,dEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

testo3dEF3vv=D[testo3,dEF3''[((E^((cFG0[v])/2))/v)]]

testo3aFG3=D[testo3,aFG3[v]]

testo3aFG3v=D[testo3,aFG3'[v]]

testo3aFG3vv=D[testo3,aFG3''[v]]

testo3bFG3=D[testo3,bFG3[v]]//Simplify

testo3bFG3v=D[testo3,bFG3'[v]]//Simplify

testo3bFG3vv=D[testo3,bFG3''[v]]

testo3dFG3=D[testo3,dFG3[v]]//Simplify

testo3dFG3v=D[testo3,dFG3'[v]]//Simplify

testo3dFG3vv=D[testo3,dFG3''[v]]

testo3: 3 order + bEF2[x]

testo3bEF2FULL=Simplify/@(Series[Normal[Simplify/@(Series[Expand[testo3bEF2//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]],{v,0,25}]//.Union[subsFLOOR,subsCOMBO])]bEF2S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

testo3AEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3AEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3AEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3AEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

testo3bEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

testo3dEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

testo3aFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3aFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3aFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3aFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

testo3bFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3bFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

testo3dFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[testo3dFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

testo3: rest

testo3rest//Expand//Length

testo3restp01=Simplify/@((Series[testo3rest[[Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp02=Simplify/@((Series[testo3rest[[100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp03=Simplify/@((Series[testo3rest[[200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp04=Simplify/@((Series[testo3rest[[300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp05=Simplify/@((Series[testo3rest[[400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp06=Simplify/@((Series[testo3rest[[500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp07=Simplify/@((Series[testo3rest[[600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp08=Simplify/@((Series[testo3rest[[700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp09=Simplify/@((Series[testo3rest[[800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp10=Simplify/@((Series[testo3rest[[900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp11=Simplify/@((Series[testo3rest[[1000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp12=Simplify/@((Series[testo3rest[[1100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp13=Simplify/@((Series[testo3rest[[1200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp14=Simplify/@((Series[testo3rest[[1300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp15=Simplify/@((Series[testo3rest[[1400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp16=Simplify/@((Series[testo3rest[[1500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp17=Simplify/@((Series[testo3rest[[1600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp18=Simplify/@((Series[testo3rest[[1700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp19=Simplify/@((Series[testo3rest[[1800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp20=Simplify/@((Series[testo3rest[[1900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp21=Simplify/@((Series[testo3rest[[2000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp22=Simplify/@((Series[testo3rest[[2100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp23=Simplify/@((Series[testo3rest[[2200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp24=Simplify/@((Series[testo3rest[[2300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp25=Simplify/@((Series[testo3rest[[2400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp26=Simplify/@((Series[testo3rest[[2500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp27=Simplify/@((Series[testo3rest[[2600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp28=Simplify/@((Series[testo3rest[[2700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp29=Simplify/@((Series[testo3rest[[2800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restp30=Simplify/@((Series[testo3rest[[2900+Range[75]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

testo3restS=Simplify/@((testo3restp01+testo3restp02+testo3restp03+testo3restp04+testo3restp05+testo3restp06+testo3restp07+testo3restp08+testo3restp09+testo3restp10+
testo3restp11+testo3restp12+testo3restp13+testo3restp14+testo3restp15+testo3restp16+testo3restp17+testo3restp18+testo3restp19+testo3restp20+
testo3restp21+testo3restp22+testo3restp23+testo3restp24+testo3restp25+testo3restp26+testo3restp27+testo3restp28+testo3restp29+testo3restp30)//.subsCOMBO)

testo3: final answer (IT WORKS UP TO ((O[v])^12))

Expand/@((testo3restS+testo3bEF2FULL+testo3AEF3FULL+testo3bEF3FULL+testo3dEF3FULL+testo3aFG3FULL+testo3bFG3FULL+testo3dFG3FULL)//.Flatten[Solve[SeriesCoefficient[Simplify/@(checko32restS+checko32bEF2FULL+checko32AEF3FULL+checko32bEF3FULL+checko32dEF3FULL+checko32aFG3FULL+checko32bFG3FULL+checko32dFG3FULL),3]==0,DFG3a]])//N//Chop

Evaluation of checko31

checko31: Dividing into parts (3 order + bEF2[x] + rest)

checko31rest=Expand[checko31//.{AEF3[((E^((cFG0[v])/2))/v)]->0,AEF3'[((E^((cFG0[v])/2))/v)]->0,AEF3''[((E^((cFG0[v])/2))/v)]->0,bEF3[((E^((cFG0[v])/2))/v)]->0,bEF3'[((E^((cFG0[v])/2))/v)]->0,bEF3''[((E^((cFG0[v])/2))/v)]->0,dEF3[((E^((cFG0[v])/2))/v)]->0,dEF3'[((E^((cFG0[v])/2))/v)]->0,dEF3''[((E^((cFG0[v])/2))/v)]->0,bEF2[((E^((cFG0[v])/2))/v)]->0,aFG3[v]->0,AFG3'[v]->0,AFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0}];

checko31bEF2=D[checko31,bEF2[((E^((cFG0[v])/2))/v)]]//Simplify

checko31AEF3=D[checko31,AEF3[((E^((cFG0[v])/2))/v)]]

checko31AEF3v=D[checko31,AEF3'[((E^((cFG0[v])/2))/v)]]

checko31AEF3vv=D[checko31,AEF3''[((E^((cFG0[v])/2))/v)]]

checko31bEF3=D[checko31,bEF3[((E^((cFG0[v])/2))/v)]]//Simplify

checko31bEF3v=D[checko31,bEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

checko31bEF3vv=D[checko31,bEF3''[((E^((cFG0[v])/2))/v)]]

checko31dEF3=D[checko31,dEF3[((E^((cFG0[v])/2))/v)]]//Simplify

checko31dEF3v=D[checko31,dEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

checko31dEF3vv=D[checko31,dEF3''[((E^((cFG0[v])/2))/v)]]

checko31aFG3=D[checko31,aFG3[v]]

checko31aFG3v=D[checko31,aFG3'[v]]

checko31aFG3vv=D[checko31,aFG3''[v]]

checko31bFG3=D[checko31,bFG3[v]]//Simplify

checko31bFG3v=D[checko31,bFG3'[v]]//Simplify

checko31bFG3vv=D[checko31,bFG3''[v]]

checko31dFG3=D[checko31,dFG3[v]]//Simplify

checko31dFG3v=D[checko31,dFG3'[v]]//Simplify

checko31dFG3vv=D[checko31,dFG3''[v]]

checko31: 3 order + bEF2[x]

checko31bEF2FULL=Simplify/@(Series[Normal[Simplify/@(Series[Expand[checko31bEF2//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]],{v,0,25}]//.Union[subsFLOOR,subsCOMBO])]bEF2S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko31AEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31AEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31AEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31AEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko31bEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko31dEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko31aFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31aFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31aFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31aFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko31bFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31bFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko31dFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko31dFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko31:rest

checko31rest//Length

checko31restp01=Simplify/@((Series[checko31rest[[Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp02=Simplify/@((Series[checko31rest[[100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp03=Simplify/@((Series[checko31rest[[200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp04=Simplify/@((Series[checko31rest[[300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp05=Simplify/@((Series[checko31rest[[400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp06=Simplify/@((Series[checko31rest[[500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp07=Simplify/@((Series[checko31rest[[600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp08=Simplify/@((Series[checko31rest[[700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp09=Simplify/@((Series[checko31rest[[800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp10=Simplify/@((Series[checko31rest[[900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp11=Simplify/@((Series[checko31rest[[1000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp12=Simplify/@((Series[checko31rest[[1100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp13=Simplify/@((Series[checko31rest[[1200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp14=Simplify/@((Series[checko31rest[[1300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp15=Simplify/@((Series[checko31rest[[1400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp16=Simplify/@((Series[checko31rest[[1500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp17=Simplify/@((Series[checko31rest[[1600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp18=Simplify/@((Series[checko31rest[[1700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp19=Simplify/@((Series[checko31rest[[1800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp20=Simplify/@((Series[checko31rest[[1900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp21=Simplify/@((Series[checko31rest[[2000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp22=Simplify/@((Series[checko31rest[[2100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp23=Simplify/@((Series[checko31rest[[2200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp24=Simplify/@((Series[checko31rest[[2300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp25=Simplify/@((Series[checko31rest[[2400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp26=Simplify/@((Series[checko31rest[[2500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp27=Simplify/@((Series[checko31rest[[2600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp28=Simplify/@((Series[checko31rest[[2700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp29=Simplify/@((Series[checko31rest[[2800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp30=Simplify/@((Series[checko31rest[[2900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp31=Simplify/@((Series[checko31rest[[3000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp32=Simplify/@((Series[checko31rest[[3100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp33=Simplify/@((Series[checko31rest[[3200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp34=Simplify/@((Series[checko31rest[[3300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp35=Simplify/@((Series[checko31rest[[3400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp36=Simplify/@((Series[checko31rest[[3500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp37=Simplify/@((Series[checko31rest[[3600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp38=Simplify/@((Series[checko31rest[[3700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp39=Simplify/@((Series[checko31rest[[3800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp40=Simplify/@((Series[checko31rest[[3900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp41=Simplify/@((Series[checko31rest[[4000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp42=Simplify/@((Series[checko31rest[[4100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp43=Simplify/@((Series[checko31rest[[4200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp44=Simplify/@((Series[checko31rest[[4300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp45=Simplify/@((Series[checko31rest[[4400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp46=Simplify/@((Series[checko31rest[[4500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp47=Simplify/@((Series[checko31rest[[4600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp48=Simplify/@((Series[checko31rest[[4700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp49=Simplify/@((Series[checko31rest[[4800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp50=Simplify/@((Series[checko31rest[[4900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp51=Simplify/@((Series[checko31rest[[5000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp52=Simplify/@((Series[checko31rest[[5100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp53=Simplify/@((Series[checko31rest[[5200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp54=Simplify/@((Series[checko31rest[[5300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restp55=Simplify/@((Series[checko31rest[[5400+Range[56]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko31restS=Simplify/@((checko31restp01+checko31restp02+checko31restp03+checko31restp04+checko31restp05+checko31restp06+checko31restp07+checko31restp08+checko31restp09+checko31restp10+
checko31restp11+checko31restp12+checko31restp13+checko31restp14+checko31restp15+checko31restp16+checko31restp17+checko31restp18+checko31restp19+checko31restp20+
checko31restp21+checko31restp22+checko31restp23+checko31restp24+checko31restp25+checko31restp26+checko31restp27+checko31restp28+checko31restp29+checko31restp30+checko31restp31+checko31restp32+checko31restp33+checko31restp34+checko31restp35+checko31restp36+checko31restp37+checko31restp38+checko31restp39+checko31restp40+checko31restp41+checko31restp42+checko31restp43+checko31restp44+checko31restp45+checko31restp46+checko31restp47+checko31restp48+checko31restp49+checko31restp50+checko31restp51+checko31restp52+checko31restp53+checko31restp54+checko31restp55)//.subsCOMBO)

checko31: final answer (IT WORKS UP TO ((O[v])^12))

(Expand/@(Simplify/@(checko31restS+checko31bEF2FULL+checko31AEF3FULL+checko31bEF3FULL+checko31dEF3FULL+checko31aFG3FULL+checko31bFG3FULL+checko31dFG3FULL))//.Flatten[Solve[SeriesCoefficient[Simplify/@(checko32restS+checko32bEF2FULL+checko32AEF3FULL+checko32bEF3FULL+checko32dEF3FULL+checko32aFG3FULL+checko32bFG3FULL+checko32dFG3FULL),3]==0,DFG3a]])//N//Chop

Evaluation of checko32

checko32: Dividing into parts (3 order + bEF2[x] + rest)

checko32rest=Expand[checko32//.{AEF3[((E^((cFG0[v])/2))/v)]->0,AEF3'[((E^((cFG0[v])/2))/v)]->0,AEF3''[((E^((cFG0[v])/2))/v)]->0,bEF3[((E^((cFG0[v])/2))/v)]->0,bEF3'[((E^((cFG0[v])/2))/v)]->0,bEF3''[((E^((cFG0[v])/2))/v)]->0,dEF3[((E^((cFG0[v])/2))/v)]->0,dEF3'[((E^((cFG0[v])/2))/v)]->0,dEF3''[((E^((cFG0[v])/2))/v)]->0,bEF2[((E^((cFG0[v])/2))/v)]->0,aFG3[v]->0,AFG3'[v]->0,AFG3''[v]->0,bFG3[v]->0,bFG3'[v]->0,bFG3''[v]->0,dFG3[v]->0,dFG3'[v]->0,dFG3''[v]->0}];

checko32bEF2=D[checko32,bEF2[((E^((cFG0[v])/2))/v)]]//Simplify

checko32AEF3=D[checko32,AEF3[((E^((cFG0[v])/2))/v)]]

checko32AEF3v=D[checko32,AEF3'[((E^((cFG0[v])/2))/v)]]

checko32AEF3vv=D[checko32,AEF3''[((E^((cFG0[v])/2))/v)]]

checko32bEF3=D[checko32,bEF3[((E^((cFG0[v])/2))/v)]]//Simplify

checko32bEF3v=D[checko32,bEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

checko32bEF3vv=D[checko32,bEF3''[((E^((cFG0[v])/2))/v)]]

checko32dEF3=D[checko32,dEF3[((E^((cFG0[v])/2))/v)]]//Simplify

checko32dEF3v=D[checko32,dEF3'[((E^((cFG0[v])/2))/v)]]//Simplify

checko32dEF3vv=D[checko32,dEF3''[((E^((cFG0[v])/2))/v)]]

checko32aFG3=D[checko32,aFG3[v]]

checko32aFG3v=D[checko32,aFG3'[v]]

checko32aFG3vv=D[checko32,aFG3''[v]]

checko32bFG3=D[checko32,bFG3[v]]//Simplify

checko32bFG3v=D[checko32,bFG3'[v]]//Simplify

checko32bFG3vv=D[checko32,bFG3''[v]]

checko32dFG3=D[checko32,dFG3[v]]//Simplify

checko32dFG3v=D[checko32,dFG3'[v]]//Simplify

checko32dFG3vv=D[checko32,dFG3''[v]]

checko32: 3 order + bEF2[x]

checko32bEF2FULL=Simplify/@(Series[Normal[Simplify/@(Series[Expand[checko32bEF2//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]],{v,0,25}]//.Union[subsFLOOR,subsCOMBO])]bEF2S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko32AEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32AEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32AEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32AEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]AEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko32bEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko32dEF3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dEF3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dEF3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S'[((Sqrt[3+(v^4)])/((Sqrt[3]) v))]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dEF3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dEF3S''[((Sqrt[3+(v^4)])/((Sqrt[3]) v))],{v,0,12}]//.subsCOMBO)

checko32aFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32aFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32aFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32aFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]aFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko32bFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32bFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]bFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko32dFG3FULL=Simplify/@(Series[Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dFG3//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dFG3v//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS'[v]+Assuming[And[v<(3^(1/4)),v>0],Refine[checko32dFG3vv//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2]//Simplify]]dFG3NEWS''[v],{v,0,12}]//.subsCOMBO)

checko32: rest

checko32rest//Length

checko32restp01=Simplify/@((Series[checko32rest[[Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp02=Simplify/@((Series[checko32rest[[100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp03=Simplify/@((Series[checko32rest[[200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp04=Simplify/@((Series[checko32rest[[300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp05=Simplify/@((Series[checko32rest[[400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp06=Simplify/@((Series[checko32rest[[500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp07=Simplify/@((Series[checko32rest[[600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp08=Simplify/@((Series[checko32rest[[700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp09=Simplify/@((Series[checko32rest[[800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp10=Simplify/@((Series[checko32rest[[900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp11=Simplify/@((Series[checko32rest[[1000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp12=Simplify/@((Series[checko32rest[[1100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp13=Simplify/@((Series[checko32rest[[1200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp14=Simplify/@((Series[checko32rest[[1300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp15=Simplify/@((Series[checko32rest[[1400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp16=Simplify/@((Series[checko32rest[[1500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp17=Simplify/@((Series[checko32rest[[1600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp18=Simplify/@((Series[checko32rest[[1700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp19=Simplify/@((Series[checko32rest[[1800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp20=Simplify/@((Series[checko32rest[[1900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp21=Simplify/@((Series[checko32rest[[2000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp22=Simplify/@((Series[checko32rest[[2100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp23=Simplify/@((Series[checko32rest[[2200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp24=Simplify/@((Series[checko32rest[[2300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp25=Simplify/@((Series[checko32rest[[2400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp26=Simplify/@((Series[checko32rest[[2500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp27=Simplify/@((Series[checko32rest[[2600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp28=Simplify/@((Series[checko32rest[[2700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp29=Simplify/@((Series[checko32rest[[2800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp30=Simplify/@((Series[checko32rest[[2900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp31=Simplify/@((Series[checko32rest[[3000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp32=Simplify/@((Series[checko32rest[[3100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp33=Simplify/@((Series[checko32rest[[3200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp34=Simplify/@((Series[checko32rest[[3300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp35=Simplify/@((Series[checko32rest[[3400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp36=Simplify/@((Series[checko32rest[[3500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp37=Simplify/@((Series[checko32rest[[3600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp38=Simplify/@((Series[checko32rest[[3700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp39=Simplify/@((Series[checko32rest[[3800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp40=Simplify/@((Series[checko32rest[[3900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp41=Simplify/@((Series[checko32rest[[4000+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp42=Simplify/@((Series[checko32rest[[4100+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp43=Simplify/@((Series[checko32rest[[4200+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp44=Simplify/@((Series[checko32rest[[4300+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp45=Simplify/@((Series[checko32rest[[4400+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp46=Simplify/@((Series[checko32rest[[4500+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp47=Simplify/@((Series[checko32rest[[4600+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp48=Simplify/@((Series[checko32rest[[4700+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp49=Simplify/@((Series[checko32rest[[4800+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp50=Simplify/@((Series[checko32rest[[4900+Range[100]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restp51=Simplify/@((Series[checko32rest[[5000+Range[104]]]//.Union[subsSOLo012wDERupto4,subsSOLFG,D[subsSOLFG,v],D[subsSOLFG,v,v],subsSOLbEF2],{v,0,20}]//.subsFLOOR)//.subsCOMBO)

checko32restS=Simplify/@((checko32restp01+checko32restp02+checko32restp03+checko32restp04+checko32restp05+checko32restp06+checko32restp07+checko32restp08+checko32restp09+checko32restp10+
checko32restp11+checko32restp12+checko32restp13+checko32restp14+checko32restp15+checko32restp16+checko32restp17+checko32restp18+checko32restp19+checko32restp20+
checko32restp21+checko32restp22+checko32restp23+checko32restp24+checko32restp25+checko32restp26+checko32restp27+checko32restp28+checko32restp29+checko32restp30+checko32restp31+checko32restp32+checko32restp33+checko32restp34+checko32restp35+checko32restp36+checko32restp37+checko32restp38+checko32restp39+checko32restp40+checko32restp41+checko32restp42+checko32restp43+checko32restp44+checko32restp45+checko32restp46+checko32restp47+checko32restp48+checko32restp49+checko32restp50+checko32restp51)//.subsCOMBO)

checko32: final answer (IT WORKS UP TO ((O[v])^12))

(Simplify/@(checko32restS+checko32bEF2FULL+checko32AEF3FULL+checko32bEF3FULL+checko32dEF3FULL+checko32aFG3FULL+checko32bFG3FULL+checko32dFG3FULL))//.Flatten[Solve[SeriesCoefficient[Simplify/@(checko32restS+checko32bEF2FULL+checko32AEF3FULL+checko32bEF3FULL+checko32dEF3FULL+checko32aFG3FULL+checko32bFG3FULL+checko32dFG3FULL),3]==0,DFG3a]]//Expand//N//Chop