Generalized Hermite polynomials and supergaussian forms
type: Item
instance of: scholarly article
title: Generalized Hermite polynomials and supergaussian forms
zbMATH Open document ID: 0872.33009
author: S. Lorenzutta
author: G. Maino
author: Clemente Cesarano
author: G. Dattoli
author: Amalia Torre
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-12-08T00:00:00Z
review text: Generalized Hermite polynomials \(H_{n,m}(x)\) were studied. Their generating function was given, association with Humbert and Gould- Hopper type polynomials, differential equations satisfied by \(H_{n,m}(x)\), recurrence properties, introduction and harmonic oscillator-like functions, nonorthogonal properties, relevant creation -- annihilation operator algebra, generalized forms of harmonic oscillator eigenfunctions were discussed. Extension of generalized Hermite polynomials leading to the class of Bell polynomials were dealt with. Super-Gauss-Hermite functions with pseudo-orthogonal properties were also discussed. They are shown for \(m=4\).
Mathematics Subject Classification ID: 33C50
zbMATH DE Number: 954700
zbMATH Keywords: orthogonal polynomials of several variables
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0399
OpenAlex ID: W2001345776
DOI: 10.1006/JMAA.1996.0399
description: scientific article; zbMATH DE number 954700