Parametric Apéry-type Series and Hurwitz-type Multiple Zeta Values
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912076310511616 |
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| author | Kaneko, Masanobu Wang, Weiping Xu, Ce Zhao, Jianqiang |
| author_facet | Kaneko, Masanobu Wang, Weiping Xu, Ce Zhao, Jianqiang |
| contents | In this paper, we extend the main results of a 2024 \emph{Advances in Applied Mathematics} paper \cite{XuZhao2021c} about Apéry-type series involving central binomial coefficients and the multiple ($t-$)harmonic sums to parametric Apéry-type series involving parametric binomial coefficients and Hurwitz-type multiple harmonic (star) sums. In particular, we will establish many explicit relations between parametric Apéry-type series involving one or two parametric binomial coefficients and Hurwitz-type multiple zeta values (with $r$-variables) by using the method of iterated integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06770 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parametric Apéry-type Series and Hurwitz-type Multiple Zeta Values Kaneko, Masanobu Wang, Weiping Xu, Ce Zhao, Jianqiang Number Theory In this paper, we extend the main results of a 2024 \emph{Advances in Applied Mathematics} paper \cite{XuZhao2021c} about Apéry-type series involving central binomial coefficients and the multiple ($t-$)harmonic sums to parametric Apéry-type series involving parametric binomial coefficients and Hurwitz-type multiple harmonic (star) sums. In particular, we will establish many explicit relations between parametric Apéry-type series involving one or two parametric binomial coefficients and Hurwitz-type multiple zeta values (with $r$-variables) by using the method of iterated integrals. |
| title | Parametric Apéry-type Series and Hurwitz-type Multiple Zeta Values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2209.06770 |