On some combinations of multiple zeta-star values

Kohtaro Imatomi, Tatsushi Tanaka, Koji Tasaka, Noriko Wakabayashi

Published 2009-12-10, updated 2010-04-21Version 2

We prove that the sum of multiple zeta-star values over all indices inserted two 2's into the string $(\underbrace{3,1, ..., 3,1}_{2n})$ is evaluated to a rational multiple of powers of $\pi^2$. We also establish certain conjectures on evaluations of multiple zeta-star values observed by numerical experiments.