Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 350120 | https://doi.org/10.1155/S1085337504306263

Gabriella Bretti, Pierpaolo Natalini, Paolo E. Ricci, "Generalizations of the Bernoulli and Appell polynomials", Abstract and Applied Analysis, vol. 2004, Article ID 350120, 11 pages, 2004. https://doi.org/10.1155/S1085337504306263

Generalizations of the Bernoulli and Appell polynomials

Received19 Jul 2002

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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