On a new family of Hermite polynomials associated to parabolic cylinder functions

Authors:
G. Dattoli;C. Cesarano
Affiliations:
ENEA--Divisione Fisica Applicata, Centro Ricerche di Frascati, C.P. 65, I-00044 Frascati, Rome, Italy;Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense, ES-28040 Madrid, Spain and Department of Mathematics, University of Ulm, Ulm, Germany and ENEA Guest
Venue:
Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Year:
2003

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Generalized Hermite polynomials associated with functions of parabolic cylinder

Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics

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Abstract

We use the integral representation method to establish the link between Hermite polynomials of ordinary nature and a family of recently introduced Hermite polynomials associated with the parabolic cylinder functions.