Two formulas for certain double and multiple polylogarithms in two variables

2024/01/06 by Kaneko, Masanobu, Tsumura, Hirofumi
#11M32 #11M99 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.03213

Abstract

We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double T-values, and some double L-values. Also presented is a connection-type formula for a two-variable multiple polylogarithm, which specializes to previously known single-variable formulas. This identity can also be regarded as a generalization of the renowned five-term relation for the dilogarithm.

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