Asymptotic Expansions and Positivity of Coefficients for Large Powers of Analytic Functions
نویسنده
چکیده
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 ∈ C, z ∉R+. 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.
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