Generalizations of the Bernoulli and Appell polynomials

Gabriella Bretti, Pierpaolo Natalini and Paolo E. Ricci

Abstract and Applied Analysis, 2004, vol. 2004, 1-11

Abstract:

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. The main properties of these polynomial sets are shown. In particular, the differential equations can be constructed by means of the factorization method.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:350120

DOI: 10.1155/S1085337504306263

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