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29 June 2004 Generalizations of the Bernoulli and Appell polynomials
Gabriella Bretti, Pierpaolo Natalini, Paolo E. Ricci
Abstr. Appl. Anal. 2004(7): 613-623 (29 June 2004). DOI: 10.1155/S1085337504306263

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.

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Gabriella Bretti. Pierpaolo Natalini. Paolo E. Ricci. "Generalizations of the Bernoulli and Appell polynomials." Abstr. Appl. Anal. 2004 (7) 613 - 623, 29 June 2004. https://doi.org/10.1155/S1085337504306263

Information

Published: 29 June 2004
First available in Project Euclid: 7 July 2004

zbMATH: 1114.33021
MathSciNet: MR2084940
Digital Object Identifier: 10.1155/S1085337504306263

Subjects:
Primary: 33C99 , 34A35

Rights: Copyright © 2004 Hindawi

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