Analytic continuation of multi-variable Arakawa-Kaneko zeta function for positive indices and its values at positive integers (Q2075026)

The author studied the analytic continuation of multi-variable Arakawa-Kaneko zeta function at positive indices and also its values at positive integers. The author gave a multi-variable generalization of the zeta function which was defined by \textit{T. Arakawa} and \textit{M. Kaneko} [Nagoya Math. J. 153, 189--209 (1999; Zbl 0932.11055)]. The author provided also the analytic continuation of this function to an entire function, whence it follows that values at non-positive integers are expressed as multi-indexed poly-Bernoulli numbers of C-type. Finally, the author not only proved that its values at positive integers are in the space spanned by multiple zeta values, but also gave some remarks, numerical evaluations and observations on this function.