A Combinatorial Identity of Multiple Zeta Values with Even Arguments

Abstract

Let $\zeta(s_1,s_2,\cdots,s_k;\alpha)$ be the multiple Hurwitz zeta function. Given two positive integers $k$ and $n$ with $k\leq n$, let $E(2n, k;\alpha)$ be the sum of all multiple zeta values with even arguments whose weight is $2n$ and whose depth is $k$.  In this note we present some generating series for the numbers $E(2n,k;\alpha)$.