On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application. (English. French summary) Zbl 1435.11043
Summary: 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.
MSC:
11B68 | Bernoulli and Euler numbers and polynomials |
11M32 | Multiple Dirichlet series and zeta functions and multizeta values |
Keywords:
poly-Bernoulli numbers; poly-Bernoulli polynomials; Arakawa-Kaneko zeta-functions; Genocchi numbersReferences:
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