Operational Methods for Hermite Polynomials-Reference-Cited by-同舟云学术

Operational Methods for Hermite Polynomials

Published:2022-03-12 Issue: Volume:16 Page:48-52
ISSN:1998-0140
Container-title:International Journal of Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:

Author:

Cesarano C.¹

Affiliation:

1. Faculty of Engineering, International Telematic University UNINETTUNO, Rome, Italy

Abstract

We exploit methods of operational nature to derive a set of new identities involving families of polynomials associated with operators providing different realizations of the Weyl group. The identities, we will deal with, extend the Nielsen formulae, valid for ordinary Hermite to families of Hermite-like polynomials. It will also be shown that the underlying formalism yields the possibility of obtaining further identities relevant to multi-variable and multi-index polynomials.

Publisher

North Atlantic University Union (NAUN)

Subject

Applied Mathematics,Computational Mathematics,Mathematical Physics,Modeling and Simulation

Reference10 articles.

1. Cesarano, C., “Monomiality Principle and related operational techniques for Orthogonal Polynomials and Special Functions”, Int. J. of Math. Models and Methods in Appl. Sci., to appear, 2014.

2. Miller, W., Lie Theory and Special functions, Academic Press, New York, 1968.

3. Cesarano, C., Assante, D., “A note on generalized Bessel functions”, Int. J. of Math. Models and Methods in Appl. Sci., 7 (6), pp 625-629, 2013.

4. Dattoli, G., Cesarano, C., “On a new family of Hermite polynomials associated to parabolic cylinder functions”, Applied Mathematics and Computation, 141 (1), pp. 143-149, 2003.

5. Appell, P., Kampé de Fériet, J., “Fonctions hypergéométriques et hypersphériques. Polinomes d’Hermite”, Gauthier-Villars, Paris, 1926.