Error bounds for the asymptotic expansion of the Hurwitz zeta function

G. Nemes

doi:10.1098/rspa.2017.0363

Error bounds for the asymptotic expansion of the Hurwitz zeta function

G. Nemes^*

^*Corresponding author for this work

University of Edinburgh

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

21 Scopus citations

Abstract

In this paper, we reconsider the large-a asymptotic expansion of the Hurwitz zeta function ς(s, a). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G-function and the s-derivative of the Hurwitz zeta function ς(s, a) are provided. A detailed discussion on the sharpness of our error bounds is also given.

Original language	English
Article number	0363
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	473
Issue number	2203
DOIs	https://doi.org/10.1098/rspa.2017.0363
State	Published - 1 Jul 2017
Externally published	Yes

Keywords

Asymptotic expansions
Barnes G-function
Error bounds
Gamma function
Hurwitz zeta function
Polygamma functions

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10.1098/rspa.2017.0363

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AB - In this paper, we reconsider the large-a asymptotic expansion of the Hurwitz zeta function ς(s, a). New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes G-function and the s-derivative of the Hurwitz zeta function ς(s, a) are provided. A detailed discussion on the sharpness of our error bounds is also given.

KW - Asymptotic expansions

KW - Barnes G-function

KW - Error bounds

KW - Gamma function

KW - Hurwitz zeta function

KW - Polygamma functions

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JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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ER -

Error bounds for the asymptotic expansion of the Hurwitz zeta function

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