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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 57, Pages 3633-3642
http://dx.doi.org/10.1155/S0161171203211133

The Hermite polynomials and the Bessel functions from a general point of view

1Unita Tecnico ScientificĂ  Tecnologie Fisiche, Gruppo Fisica Teorica e Matematica Applicata, Ente Nationale per le Nuove Tecnologie, l'Energia e l'Ambiente Via Enrico Fermi 45, Roma, Frascati 00044, Italy
2Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada
3Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro 5, Roma 00185, Italy

Received 5 November 2002

Copyright © 2003 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.

Abstract

We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show that they satisfy differential-difference equations which are isospectral to those of the ordinary case. We also indicate the usefulness of some of these new families.