Parametric Apéry-type Series and Hurwitz-type Multiple Zeta Values

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.