A Darboux-type theorem for slowly varying functions

摘要

For functions g(z) satisfying a slowly varying condition in the complex plane, we iind asymptotics For the Taylor coefficients of the function f(z) = g(z)(1-z)(-alpha) when alpha > 0. As applications we find asymptotics for the number of permutations with cycle lengths all lying in a given set S, and for the number having unique cycle lengths. (C) 1997 Academic Press