Series expansions for the Riemann zeta function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911842854502400 |
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| author | Kuznetsov, Alexey |
| author_facet | Kuznetsov, Alexey |
| contents | We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series representations of the Riemann zeta function in terms of the incomplete gamma functions, generalized hypergeometric functions and Meijer $G$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03261 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Series expansions for the Riemann zeta function Kuznetsov, Alexey Number Theory Complex Variables 11M06, 41A58 We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series representations of the Riemann zeta function in terms of the incomplete gamma functions, generalized hypergeometric functions and Meijer $G$-functions. |
| title | Series expansions for the Riemann zeta function |
| topic | Number Theory Complex Variables 11M06, 41A58 |
| url | https://arxiv.org/abs/2312.03261 |