Full asymptotic expansions of the Landau constants via a difference equation approach

Yutian LI, Saiyu Liu, Shuaixia Xu, Yuqiu Zhao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We derive full asymptotic expansions for the Landau constants G n as n → ∞. Some of the expansions are not new, yet all the coefficients of the expansions are given iteratively in an explicit manner, and are more efficiently evaluated as compared with the known results. We obtain the asymptotic formulas, old and new, by applying the theory of Wong and Li for second-order linear difference equations. In deriving the expansions, we have also confirmed a conjecture made by Nemes and Nemes.

Original languageEnglish
Pages (from-to)988-995
Number of pages8
JournalApplied Mathematics and Computation
Volume219
Issue number3
DOIs
Publication statusPublished - 15 Oct 2012

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Asymptotic expansion
  • Asymptotic solution
  • Landau constants
  • Second-order linear difference equation

Fingerprint

Dive into the research topics of 'Full asymptotic expansions of the Landau constants via a difference equation approach'. Together they form a unique fingerprint.

Cite this