Multiple zeta values and coefficients of Laurent series expansion of Beta function

Abstract

In [12], we proved a translation formula for multiple zeta functions, which is analogous to that of Riemann zeta function proved by V. Ramaswami [11]. In this article we present a nice application of this formula. Particularly we express the coefficients of Laurent series expansion of one variable Beta function $B(s,\frac{1}{2})$ in terms of certain series involving multiple zeta values. As a consequence, we are able to calculate the values of these series recursively.