@article{f97d07e0f8b04bd89552a4ff1b93b819,

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

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.",

author = "Masanobu Kaneko and Fumi Sakurai and Hirofumi Tsumura",

note = "Funding Information: Manuscrit re{\c c}u le 28 avril 2016, accept{\'e} le 12 septembre 2016. 2010 Mathematics Subject Classification. 11B68, 11M32. Mots-clefs. Poly-Bernoulli numbers, Poly-Bernoulli polynomials, Arakawa–Kaneko zeta-functions, Genocchi numbers. This work was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (S) 16H06336, (B) 23340010 and (C) 15K04788. Publisher Copyright: {\textcopyright} Soci{\'e}t{\'e} Arithm{\'e}tique de Bordeaux, 2018, tous droits r{\'e}serv{\'e}s.",

year = "2018",

doi = "10.5802/jtnb.1023",

language = "English",

volume = "30",

pages = "203--218",

journal = "Journal de Theorie des Nombres de Bordeaux",

issn = "1246-7405",

publisher = "Universite de Bordeaux III (Michel de Montaigne)",

number = "1",

}