Some results on Arakawa-Kaneko, Kaneko-Tsumura functions and related functions

Maneka Pallewattaa; Ce Xu

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arXiv · 1901.07877

Some results on Arakawa-Kaneko, Kaneko-Tsumura functions and related functions

Maneka Pallewattaa·Ce Xu

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Abstract

Recently, the level two analogue of multiple polylogarithm function ${\rm A}(k_1,\ldots,k_r;z)$ and Arakawa-Kaneko zeta function $ψ(k_1,\ldots,k_r;s)$ were introduced by M. Kaneko and H. Tsumura, for $k_1,\ldots,k_r \in \mathbb{Z}_{\ge 1}$ . In this paper, we investigate some of their special relations. In particular, we prove some explicit forms of ${\rm A}(k_1,\ldots,k_r;z)$ and $ψ(k_1,\ldots,k_r;s)$. Also, we introduce a level $m$ anlogue of the Arakawa-Kaneko zeta functions.

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BibTeX RIS

Maneka Pallewattaa, Ce Xu. 2022-09-01. Some results on Arakawa-Kaneko, Kaneko-Tsumura functions and related functions. https://arxiv.org/abs/1901.07877

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