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

Masanobu Kaneko, Fumi Sakurai, Hirofumi Tsumura

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)203-218
Number of pages16
JournalJournal de Theorie des Nombres de Bordeaux
Volume30
Issue number1
Publication statusPublished - Jan 1 2018

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Bernoulli Polynomials
Duality
Bernoulli numbers
Riemann zeta function
Generating Function
Generalise

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application. / Kaneko, Masanobu; Sakurai, Fumi; Tsumura, Hirofumi.

In: Journal de Theorie des Nombres de Bordeaux, Vol. 30, No. 1, 01.01.2018, p. 203-218.

Research output: Contribution to journalArticle

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