New Proofs of the Explicit Formulas of Arakawa--Kaneko Zeta Values and Kaneko--Tsumura $\eta$- and $\psi$- Values

TL;DR

This paper introduces new integral identities involving polylogarithms and zeta values, providing fresh proofs for explicit formulas of Arakawa--Kaneko zeta values, Kaneko--Tsumura eta- and psi-values, and a double T-value formula.

Contribution

It presents novel identities and proofs for explicit formulas of multiple zeta-related values, enhancing understanding of their structure and relationships.

Findings

New integral identities involving polylogarithms and zeta values

Alternative proofs for explicit formulas of Arakawa--Kaneko zeta values

Derived formula for double T-values

Abstract

In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the explicit formulas of Arakawa--Kaneko zeta values, Kaneko--Tsumura $\eta$- and $\psi$-values, and also give a formula for double $T$-values.