A weighted sum formula for alternating multiple zeta-star values

Abstract

In the last decade, many authors essentially contributed to the attractive theory of multiple zeta values. Nevertheless, since their introduction in 1992, there are still many hypotheses and open problems waiting to be solved. The aim of this paper is to develop a method for transforming the multiple zeta-star values. zeta*({2}(K), c) leading to a new sum formula for alternating multiple zeta-star values. Its most simple case has the intelligible form

Sigma(c-2)(t=0) (-2)(t+1) Sigma(i >= 2,s is an element of Nt)(i+vertical bar s vertical bar-c) zeta*((i) over bar, s) = (-1)(c) . zeta(c).

As a by-product, we also establish a closed form for a new harmonic-like finite summation containing binomial coefficients.