TY - JOUR
T1 - Laurent series expansions of multiple zeta-functions of Euler–Zagier type at integer points
AU - Matsumoto, Kohji
AU - Onozuka, Tomokazu
AU - Wakabayashi, Isao
N1 - Funding Information:
This research was partially supported by Grants-in-Aid for Scientific Research, Grant numbers 25287002 (for the first-named author) and 13J00312 (for the second-named author), JSPS.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00209-019-02337-2
DO - 10.1007/s00209-019-02337-2
M3 - Article
AN - SCOPUS:85068881606
VL - 295
SP - 623
EP - 642
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 1-2
ER -