Some results on Arakawa-Kaneko, Kaneko-Tsumura functions and related functions
Maneka Pallewattaa, Ce Xu

TL;DR
This paper explores special relations and explicit forms of Arakawa-Kaneko and Kaneko-Tsumura functions, introducing a level m analogue and enhancing understanding of their properties in the context of multiple polylogarithms.
Contribution
It provides explicit formulas for these functions and introduces a new level m analogue of the Arakawa-Kaneko zeta functions, expanding the theoretical framework.
Findings
Derived explicit forms of ${ m A}(k_1, dots,k_r;z)$ and $ ext{ m extpsi}(k_1, dots,k_r;s)$
Established relations between these functions and multiple polylogarithms
Introduced a level m analogue of Arakawa-Kaneko zeta functions
Abstract
Recently, the level two analogue of multiple polylogarithm function and Arakawa-Kaneko zeta function were introduced by M. Kaneko and H. Tsumura, for . In this paper, we investigate some of their special relations. In particular, we prove some explicit forms of and . Also, we introduce a level anlogue of the Arakawa-Kaneko zeta functions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Combinatorial Mathematics
