New functional equations of finite multiple polylogarithms

2017/06/28 by Masataka Ono, Ono, Masataka
Mathematics · Materials Science · Pharmacology, Toxicology and Pharmaceutics · #Advanced Mathematical Identities #Polymer Synthesis and Characterization #Pharmacy and Medical Practices

paper · pdf · doi:10.48550/arxiv.1706.09136

Abstract

We give a finite analogue of the well-known formula Li_\underbrace1, …, 1_n(t) = (1)/(n!)Li₁(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 ↔ 1 - t" type new functional equations of finite multiple polylogarithms of Ono-Yamamoto type and Sakugawa-Seki type.

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