Gauss Hypergeometric Functions, Multiple Polylogarithms, and Multiple Zeta Values

被引：6

作者：

Oi, Shu ^{[1
]}

机构：

[1] Waseda Univ, Dept Appl Math, Sch Fundamental Sci & Engn, Fac Sci & Engn,Okubo Shinjuku Ku, Tokyo 1698555, Japan

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2009年 / 45卷 / 04期

关键词：

DOUBLE SHUFFLE RELATIONS;

D O I：

10.2977/prims/1260476650

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we express solutions of the Gauss hypergeometric equation as a series of the multiple polylogarithms by using iterated integral. This representation is the most simple case of a semisimple representation of solutions of the formal KZ equation. Moreover, combining this representation with the connection relations of solutions of the Gauss hypergeometric equation, we obtain various relations of the multiple polylogarithms of one variable and the multiple zeta, values.

引用

页码：981 / 1009

页数：29

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