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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.
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 language | English |
|---|---|
| Number of pages | 16 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 473 |
| Issue number | 2203 |
| DOIs | |
| Publication status | Published - 5 Jul 2017 |
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Dive into the research topics of 'Error bounds for the asymptotic expansion of the Hurwitz zeta function'. Together they form a unique fingerprint.Projects
- 1 Finished
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Rigorous and Presentable Asymptotics for Special Functions and Orthogonal Polynomials
1/09/15 → 31/08/20
Project: Research