Explicit evaluation of certain sums of multiple zeta-star values

Shuji Yamamoto

Published 2012-03-06Version 1

Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3,1,3,1,...,3,1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star values and showed that this value is a rational multiple of a power of \pi. In this paper, we give an explicit formula for the rational part. In addition, we interpret the result as an identity in the harmonic algebra.