Values at non-positive integers of generalized Euler-Zagier multiple zeta-functions

Driss Essouabri; Kohji Matsumoto

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arXiv · 1703.07525

Values at non-positive integers of generalized Euler-Zagier multiple zeta-functions

Driss Essouabri·Kohji Matsumoto

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Abstract

We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions and then use the analyticity of the values on the parameters defining the multiple zeta-functions to deduce the formulas in the general case. Also, for our aim we prove an extension of "Raabe's lemma" due to E. Friedman and A. Pereira.

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BibTeX RIS

Driss Essouabri, Kohji Matsumoto. 2017-03-22. Values at non-positive integers of generalized Euler-Zagier multiple zeta-functions. https://arxiv.org/abs/1703.07525

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