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2020 New functional equations of finite multiple polylogarithms
Masataka Ono
Tohoku Math. J. (2) 72(1): 149-157 (2020). DOI: 10.2748/tmj/1585101625

Abstract

We give a finite analogue of the well-known formula $\mathrm{Li}_{\underbrace{1, \ldots, 1}_n}(t)=\frac{1}{n!}\mathrm{Li}_1(t)^n$ of multiple polylogarithms for any positive integer $n$ by using the shuffle relation of finite multiple polylogarithms of Ono–Yamamoto type. Unlike the usual case, the terms regarded as error terms appear in this formula. As a corollary, we obtain “$t \leftrightarrow 1-t$” type new functional equations of finite multiple polylogarithms of Ono–Yamamoto type and Sakugawa-Seki type.

Citation

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Masataka Ono. "New functional equations of finite multiple polylogarithms." Tohoku Math. J. (2) 72 (1) 149 - 157, 2020. https://doi.org/10.2748/tmj/1585101625

Information

Published: 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07199991
MathSciNet: MR4079428
Digital Object Identifier: 10.2748/tmj/1585101625

Subjects:
Primary: 11M32

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 1 • 2020
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