On a \(q\)-extension of the Hermite polynomials \(H_n(x)\) with the continuous orthogonality property on \(\mathbb{R}\)
type: Item
instance of: scholarly article
title: On a \(q\)-extension of the Hermite polynomials \(H_n(x)\) with the continuous orthogonality property on \(\mathbb{R}\)
zbMATH Open document ID: 1024.33015
author: D. Massart
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2003-11-14T00:00:00Z
review text: The authors solve the following problem: To find \(q\)-extensions of the Hermite polynomials \(H_n\), \(n\in \mathbb{N}_0\) with the properties (i) they obey a three-term recurrence relation, (ii) they are orthogonal on the real line with respect to a continuous positive weight function, (iii) in the limit case \(q\to 1\) they coincide with the Hermite polynomials \(H_n\). It appears that these extensions can be expressed either in terms of the \(q\)-Laguerre polynomials of order \(\alpha-\pm 1/2\) or in terms of the discrete \(q\)-Hermite polynomials of order II.
reviewed by: Hans-Jürgen Glaeske
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 1933096
zbMATH Keywords: \(q\)-Hermite polynomials
zbMATH Keywords: orthogonality
zbMATH Keywords: three-term recurrence relation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1933096