Shows the analytical continuation and duality properties of the Arakawa-Kaneko zeta function for non-positive integers, implying deeper numerical relationships.
The multi-variable Arakawa-Kaneko zeta function is defined in a suitable way.This function can be regarded as the one to be paired up with the multi-variable function defined by Kaneko and Tsumura.It is shown that the multi-variable Arakawa-Kaneko zeta function is analytically continued to an entire function, and its values at nonpositive integers satisfy a certain duality formula which is a generalization of that for the poly-Bernoulli numbers of C-type.
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Ito Kunihiro (2020) studied this question.
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