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

Kohji Matsumoto, Tomokazu Onozuka, Isao Wakabayashi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)623-642
Number of pages20
JournalMathematische Zeitschrift
Volume295
Issue number1-2
DOIs
Publication statusPublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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