Parametric Ap\'{e}ry-type Series and Hurwitz-type Multiple Zeta Values
Number Theory
2024-10-22 v3
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 ()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 -variables) by using the method of iterated integrals.
Cite
@article{arxiv.2209.06770,
title = {Parametric Ap\'{e}ry-type Series and Hurwitz-type Multiple Zeta Values},
author = {Masanobu Kaneko and Weiping Wang and Ce Xu and Jianqiang Zhao},
journal= {arXiv preprint arXiv:2209.06770},
year = {2024}
}
Comments
33 pages