Poly-Bernoulli numbers from shifted log-sine integrals

Abstract

In 1999, Arakawa and Kaneko introduced a zeta function connecting multiple zeta values with poly-Bernoulli numbers through its special values. Log-sine integrals are also known to be related to zeta values at positive integers. In this article, we study the values of a shifted log-sine integral at negative integers and establish a connection with anti-diagonal sums of poly-Bernoulli numbers. This gives a refinement of Stephan's observation on the central binomial series.

arXiv comment7 pages