On the sum relation of multiple Hurwitz zeta functions

Abstract

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\mathbf{\alpha })$ and define similarly the multiple star $t$-values as $t^{\star }(\mathbf{\alpha })$. Then we consider the sum of all such multiple (star) $t$-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of $t(\{2m{\}}^n)$ and $t^{\star }(\{2m{\}}^n)$ are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.

7 pages