Arakawa-Kaneko L-functions and generalized poly-Bernoulli polynomials |
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Authors: | Abdelmejid Bayad |
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Institution: | a Département de mathématiques, Université d?Évry Val d?Essonne, Bd. F. Mitterrand, 91025 Évry Cedex, France b Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan |
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Abstract: | We introduce and investigate generalized poly-Bernoulli numbers and polynomials. We state and prove several properties satisfied by these polynomials. The generalized poly-Bernoulli numbers are algebraic numbers. We introduce and study the Arakawa-Kaneko L-functions. The non-positive integer values of the complex variable s of these L-functions are expressed rationally in terms of generalized poly-Bernoulli numbers and polynomials. Furthermore, we prove difference and Raabe?s type formulae for these L-functions. |
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Keywords: | 11B73 11A07 |
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