Proofs of two conjectures on the Landau constants

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Nemes, Gergo

关键词: Asymptotic expansions;    Hypergeometric Function;    Landau constants;   

DOI  :  10.1016/j.jmaa.2011.10.004

来源: Elsevier

【 摘 要 】

In this paper we derive a family of asymptotic expansions for the nth Landau constant G(n). The proof is based on a new general integral representation of the constants in terms of a Hypergeometric Function. As a consequence we prove two conjectures related to earlier asymptotic developments of the G(n)'s. (C) 2011 Elsevier Inc. All rights reserved.

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