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

Kohji Matsumoto, Tomokazu Onozuka, Isao Wakabayashi

研究成果: ジャーナルへの寄稿学術誌査読

2 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)623-642
ページ数20
ジャーナルMathematische Zeitschrift
295
1-2
DOI
出版ステータス出版済み - 6月 1 2020

!!!All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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