On the convolutions of sums of multiple zeta(-star) values of height one

Abstract

In this paper, we investigate the sums of mutliple zeta(-star) values of height one:In particular, we prove that the weighted sum 0≤m≤p m:even |α|=p+3 2 α m+1 +1 ζ(α 0 , α 1 , . . . , αm, α m+1 + 1) can be evaluated through the convolution of Z − (m) and Z + (n) with m + n = p.

Weighted Sum Formulas from Shuffle Products of Multiple Zeta-star Values

“…Both Z − (n), and Z ⋆ + (n) are sums of multiple zeta(-star) values of height one and can be expressed as double integrals (see [6])…”