Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers

Abstract

We consider a multi-variable generalization of the zeta function defined by Arakawa and Kaneko. We establish its analytic continuation to an entire function,whence it follows that values at non-positive integersare expressed as multi-indexed poly-Bernoulli numbers of C-type. We also prove that its values at positive integers are in the space spanned by multiple zeta values.