Abstract and Applied Analysis
Volume 2004 (2004), Issue 7, Pages 613-623
doi:10.1155/S1085337504306263
Generalizations of the Bernoulli and Appell polynomials
1Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università degli Studi di Roma “La Sapienza”, Roma 00161, Italy
2Dipartimento di Matematica, Università degli Studi Roma Tre, Roma 00146, Italy
3Dipartimento di Matematica, Istituto “Guido Castelnuovo”, Università degli Studi di Roma “La Sapienza”, Roma 00185, Italy
Received 19 July 2002
Copyright © 2004 Gabriella Bretti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.