A Combinatorial Identity of Multiple Zeta Values with Even Arguments

DOI: https://doi.org/10.37236/3923

Keywords: Multiple zeta values, Recursion algorithm, Generating series

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

$E(2n,k;\alpha)$ .