Estimating the \(k\)th coefficient of \((f(z))^{n}\) when \(k\) is not too large

DOI10.1016/j.jmaa.2007.01.017zbMath1124.30005OpenAlexW2064312800MaRDI QIDQ996915

Valerio de Angelis

Publication date: 19 July 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.01.017

zbMATH Keywords

multinomial coefficientsasymptotic for coefficientslarge powers of polynomials

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Power series (including lacunary series) in one complex variable (30B10) Asymptotic representations in the complex plane (30E15)

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic expansions and positivity of coefficients for large powers of analytic functions
• Some results on the asymptotic behaviour of coefficients of large powers of functions
• Analytic methods in asymptotic enumeration
• On the unimodality of high convolutions of discrete distributions
• A characterization of the maximum modulus of functions regular at the origin
• Asymptotic Expansions
• A Generalisation of Stirling's Formula.
• Asymptotic Expansions II
• Positivity conditions for polynomials
• On the Inequality | p(z) | ≤p ( | z | ) for Polynomials