Representations for the first associated \(q\)-classical orthogonal polynomials
type: Item
instance of: scholarly article
title: Representations for the first associated \(q\)-classical orthogonal polynomials
zbMATH Open document ID: 1024.33014
DOI: 10.1016/S0377-0427(02)00668-4
author: Stanisław Lewanowicz
published in: Journal of Computational and Applied Mathematics
publication date: 2003-03-11T00:00:00Z
review text: In the present paper the author considers the expansion of the first associated \(q\)-classical polynomials \(p_n^{(1)}(x;q)\) in term of the basis \(x^k\) or \((x;q)_k\) , \(k\geq 0\), and also in term of the \(q\)-classical polynomials \(p_n(x;q)\) theirselves, i.e. the problem \[ p_n^{(1)}(x;q)=\sum_{k=0}^n c_{n,k} r(x;q), \] where \(r(x;q)=x^k\), \((x;q)_k\) or \(p_n(x;q)\). In the paper the explicit formulas for the coefficients \(c_{n;k}\) and also the recurrence relations involving these connection coefficients. The case of little and big \(q\)-Jacobi polynomials are considered in details.
Mathematics Subject Classification ID: 33D45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1879846
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: associated orthogonal polynomials
zbMATH Keywords: \(q\)-classical polynomials
zbMATH Keywords: connection problem
reviewed by: Renato Álvarez-Nodarse
MaRDI profile type: Publication
cites work: \(q\)-classical polynomials and the \(q\)-Askey and Nikiforov-Uvarov tableaus
cites work: Fourth order \(q\)-difference equation for the first associated of the \(q\)-classical orthogonal polynomials
cites work: Q4040884
cites work: Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
cites work: Q4327870
cites work: Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials
cites work: On the \(q\)-polynomials: A distributional study
cites work: A q-integral representation of Rogers' q-ultraspherical polynomials and some applications
full work available at URL: s0377-0427(02)00668-4
OpenAlex ID: W2140335697
description: scientific article; zbMATH DE number 1879846