Import["https://th.if.uj.edu.pl/~odrzywolek/aa/Lane-Emden.m"]

w[4][2] (* wartość funkcji (Subscript[w, 4])(2)=0.6229407875154804 *)

Plot[{w[3][x],slope[3](x-zero[3])},{x,0,2zero[3]}] (* wykres funkcji (Subscript[w, 3])(x) z wyjaśnieniem znaczenia funkcji zero[n], slope[n] *)

w[1/2]''[1]

(* Odtworzenie TABLE C.1, APPENDIX C, str. 552, David Arnett, Supernovae & Nucleosynthesis *)

c=Function[n,-1/(n+1)/zero[n]/ slope[n]];

δρ=Function[n,-1/3zero[n]/slope[n]];

d=Function[n,c[n](4Pi/3 /δρ[n])^(1/3)];

Table[{n,zero[n], -zero[n]^2 slope[n],δρ[n], c[n],d[n]},{n,{0,1,3/2,3,3.25,4,5}}]//TableForm

Plot[c[n],{n,0,4},PlotRange->{0,2},AxesLabel->{"n","(Subscript[C, n])"},BaseStyle->{Large},PlotStyle->{Black,Thick},ImageSize->300]

Export["Cn.png",%,ImageResolution->600]