Parametric Ap\'ery-type Series and Hurwitz-type Multiple Zeta Values
Abstract
In this paper, we extend the main results of a 2024 Advances in Applied Mathematics paper XuZhao2021c about Ap\'ery-type series involving central binomial coefficients and the multiple (t-)harmonic sums to parametric Ap\'ery-type series involving parametric binomial coefficients and Hurwitz-type multiple harmonic (star) sums. In particular, we will establish many explicit relations between parametric Ap\'ery-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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