ASYMPTOTIC EXPANSIONS AND POSITIVITY OF COEFFICIENTS FOR LARGE POWERS OF ANALYTIC FUNCTIONS
ASYMPTOTIC EXPANSIONS AND POSITIVITY OF COEFFICIENTS FOR LARGE POWERS OF ANALYTIC FUNCTIONS
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大幂解析函数的渐近展开和系数的正性
DOI：
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发表时间：
2003
期刊：
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通讯作者：
V. Angelis
中科院分区：
文献类型：
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作者：
V. Angelis
本文对（f（z））n的大范围系数，w导出了当n →∞时的渐近展开式，其中f（z）是满足|f（z）|<f（|z|对于z ∈ C，z <$R + .W henf是一个多项式，且f中出现的两个最小和两个最大指数是连续的整数，我们利用这个展开式推广了Odlyzko和里士满（1985）关于多项式的对数幂的结果，并证明了f的幂只有正系数.
We derive an asymptotic expansion as n →∞ for a large range of coefficients of (f (z)) n ,w here f( z) is a power series satisfying | f( z)| <f (|z|) for z ∈ C, z ∉R + .W henf 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.