New Proofs of the Explicit Formulas of Arakawa--Kaneko Zeta Values and Kaneko--Tsumura η- and ψ- Values

2025/01/20 by Kaneko, Masanobu, Wang, Weiping, Xu, Ce +1
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.11303

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 η- and ψ-values, and also give a formula for double T-values.

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