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

2023/10/11 by Kyosuke Nishibiro, Nishibiro, Kyosuke
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #Primary 11M32 #Secondary 11B68

paper · pdf · doi:10.48550/arxiv.2310.07318

openalex publication_date 2023/10/11 · openalex created_date 2023/10/13 · openalex updated_date 2026/07/28

Abstract

Kaneko and Tsumura introduced the Arakawa-Kaneko type zeta function η(-k₁,…,-k_r;s₁,…,s_r) for non-negative integers k₁,…,k_r and complex variables s₁,…,s_r. Recently, Yamamoto showed that, by using the multiple integral expression, η(u₁,…,u_r;s₁,…,s_r) can be extended to an analytic function of 2r variables. Also, he showed that the function η(u₁,…,u_r;s₁,…,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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