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

Abstract

We give new closed and explicit formulas for zeta 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.