多重ζ值与迭代LOG-SINE积分

Pub Date : 2019-04-22 DOI:10.2206/kyushujm.74.233

Ryo Umezawa

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引用次数: 2

摘要

我们引入了（广义）对数正弦积分（迭代对数正弦积分）的迭代积分版本，并证明了多重多对数与迭代对数正弦积之间的关系。我们还给出了一种利用迭代对数正弦积分获得多个ζ值之间关系的新方法，并给出了与多个ζ值和对数正弦积分有关的几个已知结果的替代证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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MULTIPLE ZETA VALUES AND ITERATED LOG-SINE INTEGRALS

We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining relations among multiple zeta values, which uses iterated log-sine integrals, and give alternative proofs of several known results related to multiple zeta values and log-sine integrals.

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