On certain harmonic zeta functions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866916156839821312 |
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| author | Can, Mümün Kargın, Levent Cenkci, Mehmet Dil, Ayhan |
| author_facet | Can, Mümün Kargın, Levent Cenkci, Mehmet Dil, Ayhan |
| contents | This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negative even integers are found and Laurent expansions at poles are described. Closed-form expressions are derived for the Stieltjes constants that occur in Laurent expansions in a neighborhood of s=1. Moreover, as a bonus, it is obtained that the values at the positive odd integers of three harmonic zeta functions can be expressed in closed-form evaluations in terms of zeta values and log-sine integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On certain harmonic zeta functions Can, Mümün Kargın, Levent Cenkci, Mehmet Dil, Ayhan Number Theory Complex Variables 11Y60, 11M41, 11M06, 11B83, 30B40, 11B68 This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negative even integers are found and Laurent expansions at poles are described. Closed-form expressions are derived for the Stieltjes constants that occur in Laurent expansions in a neighborhood of s=1. Moreover, as a bonus, it is obtained that the values at the positive odd integers of three harmonic zeta functions can be expressed in closed-form evaluations in terms of zeta values and log-sine integrals. |
| title | On certain harmonic zeta functions |
| topic | Number Theory Complex Variables 11Y60, 11M41, 11M06, 11B83, 30B40, 11B68 |
| url | https://arxiv.org/abs/2403.07123 |