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arXiv · 2401.03213

Two formulas for certain double and multiple polylogarithms in two variables

Masanobu Kaneko·Hirofumi Tsumura
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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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Masanobu Kaneko, Hirofumi Tsumura. 2024-01-06. Two formulas for certain double and multiple polylogarithms in two variables. https://arxiv.org/abs/2401.03213

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