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arXiv · 2310.07318

On generalization of duality formulas for the Arakawa-Kaneko type zeta functions

Kyosuke Nishibiro
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Abstract

Kaneko and Tsumura introduced the Arakawa-Kaneko type zeta function $\eta(-k_1,\ldots,-k_r;s_1,\ldots,s_r)$ for non-negative integers $k_1,\ldots,k_r$ and complex variables $s_1,\ldots,s_r$. Recently, Yamamoto showed that, by using the multiple integral expression, $\eta(u_1,\ldots,u_r;s_1,\ldots,s_r)$ can be extended to an analytic function of 2$r$ variables. Also, he showed that the function $\eta(u_1,\ldots,u_r;s_1,\ldots,s_r)$ satisfies a duality formula. In this paper, by using the a generalization of non-strict multi-indexed polylogarithm, we define a kind of Arakawa-Kaneko type zeta function, and show that this function satisfies a certain duality formula.

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Kyosuke Nishibiro. 2023-10-11. On generalization of duality formulas for the Arakawa-Kaneko type zeta functions. https://arxiv.org/abs/2310.07318

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