\(q\)-coherent pairs and \(q\)-orthogonal polynomials
type: Item
instance of: scholarly article
title: \(q\)-coherent pairs and \(q\)-orthogonal polynomials
zbMATH Open document ID: 1020.33005
DOI: 10.1016/S0096-3003(01)00072-8
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The concept of \(q\)-coherent pair of linear functionals is introduced and it is proved that if \((u_0,u_1)\) is a coherent pair, then both \(u_0\) and \(u_1\) are \(q\)-semiclassical linear functionals. It is also proved that if \((u_0,u_1)\) is a \(q\)-coherent pair of linear functionals, then at least one of them must be a \(q\)-classical linear functional. The classification of all \(q\)-coherent pairs of positive-definite linear functionals \((u_0,u_1)\) when \(u_0\) or \(u_1\) is either the little \(q\)-Jacobi linear functional or the little \(q\)-Laguerre linear functional is given. Finally, by using limit relations, the classification of all coherent pairs of positive definite linear functionals is recovered.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 1861069
zbMATH Keywords: \(q\)-coherence
zbMATH Keywords: \(q\)-Jacobi polynomials
zbMATH Keywords: \(q\)-Laguerre polynomials
zbMATH Keywords: \(q\)-orthogonal polynomials
author: Iván Area
author: Eduardo Godoy
author: Francisco Marcellán
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00072-8
OpenAlex ID: W2028730210
description: scientific article; zbMATH DE number 1861069