Inner products involving \(q\)-differences: The little \(q\)-Laguerre-Sobolev polynomials
type: Item
instance of: scholarly article
title: Inner products involving \(q\)-differences: The little \(q\)-Laguerre-Sobolev polynomials
zbMATH Open document ID: 0957.33008
DOI: 10.1016/S0377-0427(00)00278-8
published in: Journal of Computational and Applied Mathematics
publication date: 2000-10-26T00:00:00Z
review text: Polynomials are considered that are orthogonal with respect to the inner product \(\langle p,r\rangle_S=\sum_{k=0}^\infty p(q^k)r(q^k){(aq)^k(aq;q)_\infty\over (q;q)_k }+\lambda\sum_{k=0}^\infty (D_qp)(q^k)(D_qr)(q^k) {(aq)^k(aq;q)_\infty\over (q;q)_k }\), where \(D_q\) is the \(q\)-difference operator, \(\lambda\geq 0\), \(0<q<1\) and \(0<aq<1\). For these polyonomials \(q\)-difference equations are obtained and their relation with the monic \(q\)-Laguerre polynomials. Some properties of the zeros of the polynomials and some asymptotic properties are given.
reviewed by: Nico M. Temme
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1472328
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Sobolev orthogonal polynomials
zbMATH Keywords: little \(q\)-Laguerre polynomials
author: Iván Area
author: Eduardo Godoy
author: Francisco Marcellán
author: J. J. Moreno-Balcázar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472328