Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points

被引：5

作者：

Matsumoto, Kohji ^{[1
]}

Onozuka, Tomokazu ^{[2
]}

Wakabayashi, Isao ^{[3
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

[2] Kyushu Univ, Multiple Zeta Res Ctr, Nishi Ku, Fukuoka 8190395, Japan

[3] Seikei Univ, Musashino, Tokyo 1808633, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 295卷 / 1-2期

基金：

日本学术振兴会;

关键词：

ANALYTIC CONTINUATION; VALUES;

D O I：

10.1007/s00209-019-02337-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give explicit expressions (or at least an algorithm to obtain such expressions) of the coefficients of the Laurent series expansions of the Euler-Zagier multiple zeta-functions at any integer points. The main tools are the Mellin-Barnes integral formula and the harmonic product formulas. The Mellin-Barnes integral formula is used in the induction process on the number of variables, and the harmonic product formula is used to show that the Laurent series expansion outside the domain of convergence can be obtained from that inside the domain of convergence.

引用

页码：623 / 642

页数：20

共 21 条

[1] Laurent series expansions of multiple zeta-functions of Euler–Zagier type at integer points
Kohji Matsumoto
Tomokazu Onozuka
Isao Wakabayashi
Mathematische Zeitschrift, 2020, 295 : 623 - 642
[2] On the estimation of the order of Euler-Zagier multiple zeta-functions
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[10] Multiple zeta functions at regular integer points
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