### 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 language | English |
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Pages (from-to) | 203-218 |

Number of pages | 16 |

Journal | Journal de Theorie des Nombres de Bordeaux |

Volume | 30 |

Issue number | 1 |

Publication status | Published - Jan 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal de Theorie des Nombres de Bordeaux*,

*30*(1), 203-218.

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

Research output: Contribution to journal › Article

*Journal de Theorie des Nombres de Bordeaux*, vol. 30, no. 1, pp. 203-218.

}

TY - JOUR

T1 - On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application

AU - Kaneko, Masanobu

AU - Sakurai, Fumi

AU - Tsumura, Hirofumi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85047269740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047269740&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85047269740

VL - 30

SP - 203

EP - 218

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

SN - 1246-7405

IS - 1

ER -