Abstract

We derive an asymptotic expansion as n for a large range of coefficients of (f(z))n, where f(z) is a power series satisfying |f(z)|<f(|z|) for z, z+. When f is a polynomial and the two smallest and the two largest exponents appearing in f are consecutive integers, we use the expansion to generalize results of Odlyzko and Richmond (1985) on log concavity of polynomials, and we prove that a power of f has only positive coefficients.