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arXiv · 2209.06770

Parametric Ap\'{e}ry-type Series and Hurwitz-type Multiple Zeta Values

Masanobu Kaneko·Weiping Wang·Ce Xu·Jianqiang Zhao
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Abstract

In this paper, we extend the main results of a 2024 \emph{Advances in Applied Mathematics} paper \cite{XuZhao2021c} about Ap\'{e}ry-type series involving central binomial coefficients and the multiple ($t-$)harmonic sums to parametric Ap\'{e}ry-type series involving parametric binomial coefficients and Hurwitz-type multiple harmonic (star) sums. In particular, we will establish many explicit relations between parametric Ap\'{e}ry-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.

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Masanobu Kaneko, Weiping Wang, Ce Xu, Jianqiang Zhao. 2022-09-12. Parametric Ap\'{e}ry-type Series and Hurwitz-type Multiple Zeta Values. https://arxiv.org/abs/2209.06770

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