International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 57, Pages 3633-3642
doi:10.1155/S0161171203211133
The Hermite polynomials and the Bessel functions from a general point of view
1Unita Tecnico Scientificà Tecnologie Fisiche, Gruppo Fisica Teorica e Matematica Applicata, Ente Nationale per le Nuove Tecnologie, l'Energia e l'Ambiente Via Enrico Fermi 45, Roma 00044, Frascati, Italy
2Department of Mathematics and Statistics, University of Victoria, Victoria V8W 3P4, British Columbia, 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 G. Dattoli 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 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.