@lisyarus@j_bertolotti in @eniko's formula there's a linear interpolation by c^2 with c = 1 - sqrt(1 - x^2) and even better results are achieved with c^1.95, so I was wondering what happens with c^2 replaced by its Taylor expansion to order 8. Or given that it should only have even terms (so order 8 would be 4 terms) maybe even up to 6 or 7 terms