Abstract Using a series of fractional powers we present representation the solution to logistic equation is presented. To simplify consider simplest case and prove that power indeed exact solution. Some numerical approximations are presented show good obtained by truncating series.

We present some observations on the asymptotic behaviour of coefficients in Laurent series expansion solutions first Painleve equation. For general solution, explicit recursive formulae for Taylor tau-function around a zero are given, which natural extensions analogous elliptic sigma function, as given by Weierstrass. Numerical and exact results symmetric solution is singular at origin also pre...