On some combinations of multiple zeta-star values

Abstract

We prove that the sum of multiple zeta-star values over all indices inserted two 2's into the string $(\underset{2n}{\underbrace{3,1,...,3,1}})$ 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.

14 pages

References in corpus (1)

• The Bowman-Bradley theorem for multiple zeta-star values

Cited by in corpus (2)

• The Bowman-Bradley theorem for multiple zeta-star values
• Identity Families of Multiple Harmonic Sums and Multiple Zeta (Star) Values