### 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 |

DOIs | |

Publication status | Published - 2018 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Kaneko, M., Sakurai, F., & Tsumura, H. (2018). On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application.

*Journal de Theorie des Nombres de Bordeaux*,*30*(1), 203-218. https://doi.org/10.5802/jtnb.1023