Asymptotic expansions and positivity of coefficients for large powers of analytic functions

Valerio De Angelis

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-23

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 ∈ 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:191950

DOI: 10.1155/S0161171203205056

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