Error bounds for the asymptotic expansion of the Hurwitz zeta function

Gergo Nemes

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we reconsider the large-a asymptotic expansion of the Hurwitz zeta
function ζ (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 ζ (s, a) are provided. A detailed discussion on the sharpness of our error bounds is also given.
Original languageEnglish
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume473
Issue number2203
DOIs
Publication statusPublished - 5 Jul 2017

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