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

TL;DR

This paper derives recurrence relations for Euler-Apéry type multiple zeta star values and their variants, enabling explicit evaluations and advancing understanding of these special mathematical constants.

Contribution

It introduces new recurrence relations for Euler-Apéry type multiple zeta star values and their parametric variants, leading to explicit evaluations.

Findings

Derived several recurrence relations for Euler-Apéry type multiple zeta star values.

Obtained explicit evaluations for specific Euler-Apéry type multiple zeta star values.

Extended results to Euler-Apéry type 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.