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On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application

2016/04/03 by Masanobu Kaneko, Kaneko, Masanobu, Fumi Sakurai +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11B68 #Secondary 11M32

paper · pdf · doi:10.48550/arxiv.1604.00622

openalex publication_date 2016/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is apparent. Secondly we give an analytic proof of the duality from the viewpoint of our previous study of zeta-functions of Arakawa-Kaneko type. As an application, we give a formula that relates poly-Bernoulli numbers to the Genocchi numbers.

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