On level two analogue of Arakawa-Kaneko zeta function and poly-cosecant numbers

Abstract

We study the level two generalization of Arakawa-Kaneko zeta function originally studied by T. Arakawa and M. Kaneko. We obtain certain new formulas for the level two analogue of Arakawa-Kaneko zeta function. Also, we study the level two generalization of poly-Bernoulli numbers, which is referred to as the poly-cosecant numbers. We obtain a recurrence and two explicit formulas for poly-cosecant numbers. Moreover, we extend those formulas for multiple versions in a similar manner. The latter part is a part of a joint work with M. Kaneko and H. Tsumura