Proofs of two conjectures on the Landau constants

Gergo Nemes

doi:10.1016/j.jmaa.2011.10.004

Proofs of two conjectures on the Landau constants

Gergo Nemes^*

^*Corresponding author for this work

Eötvös Loránd University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	838-844
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	388
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.10.004
State	Published - 15 Apr 2012
Externally published	Yes

Keywords

Asymptotic expansions
Hypergeometric function
Landau constants

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10.1016/j.jmaa.2011.10.004

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title = "Proofs of two conjectures on the Landau constants",

abstract = "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.",

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AB - 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.

KW - Asymptotic expansions

KW - Hypergeometric function

KW - Landau constants

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DO - 10.1016/j.jmaa.2011.10.004

M3 - 文章

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SN - 0022-247X

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SP - 838

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Proofs of two conjectures on the Landau constants

Abstract

Keywords

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