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

Abstract

In this paper, we will establish many explicit relations between parametric Apérytype series involving one or two parametric binomial coefficients and Hurwitz-type multiple zeta values (with r-variables) by using the method of iterated integral. Furthermore, we also establish some new identities of integrals involving multiple polylogarithm functions and Kaneko-Tsumura A-functions in terms of Hurwitz-type multiple zeta values. Then, using these formulas obtained, we obtain the explicit formulas of Arakawa-Kaneko zeta values and Kaneko-Tsumura ψ-values. Moreover, we can find a symmetric formula of Kaneko-Tsumura's conjecture about double Tvalues. Finally, we define and discuss the Hurwitz-type multiple zeta values of parametric binomial coefficient.