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

G. Dattoli,1 H. M. Srivastava,2 and D. Sacchetti3

 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

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.