Explicit Evaluation of Euler-Ap\'ery Type Multiple Zeta Star Values and Multiple $t$-Star Values

Abstract

In this paper we establish several recurrence relations about Euler-Ap\'ery type multiple zeta star values and a parametric variant of it by using the method of iterated integrals. Then using the formulas obtained, we find the explicit evaluations for some specific Euler-Ap\'ery type multiple zeta star values and one of its parametric variant, and Euler-Ap\'ery type multiple $t$-star values.