一元多聚对数及其$q$-类似物的对偶性

Pub Date : 2020-10-12 DOI:10.3836/tjm/1502179378

Shuji Yamamoto

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引用次数: 2

摘要

Hirose、Iwaki、Sato和Tasaka用迭代积分的方法证明了一元多聚对数的对偶关系。本文利用Seki和作者最近发明的连通和方法给出了一个新的证明。有趣的是，连通和在其连接符中包含超几何函数。此外，我们还引入了一元多幂算法的两类$q$-类似物，并将对偶推广到它们。

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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Duality of One-variable Multiple Polylogarithms and Their $q$-analogues

The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka by means of iterated integrals. In this paper, we give a new proof using the method of connected sums, which was recently invented by Seki and the author. Interestingly, the connected sum involves the hypergeometric function in its connector. Moreover, we introduce two kinds of $q$-analogues of the one-variable multiple poylogarithms and generalize the duality to them.

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