Transverse limits in the Askey tableau
type: Item
instance of: scholarly article
title: Transverse limits in the Askey tableau
zbMATH Open document ID: 0936.33004
DOI: 10.1016/S0377-0427(98)00167-8
author: A. Zarzo
author: A. Ronveaux
author: Iván Area
author: Eduardo Godoy
published in: Journal of Computational and Applied Mathematics
publication date: 2000-05-09T00:00:00Z
review text: Limit relations between classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk, Hahn) to classical continuous orthogonal polynomials (Jacobi, Laguerre, Hermite) -- so-called tranverse limits -- can be described by relations of type \(\lim_{\omega\rightarrow 0}P_n(x(s,\omega))=Q_n(s)\) where \(P_n(x)\) and \(Q_n(x)\) correspond to the discrete and continuous family, respectively. The authors consider the expansions \(P_n(x(s,\omega))=\sum_{k=0}^\infty R_k(s;n)\omega^k\), and develop a method to compute the coefficients \(R_k(s;n)\) by using certain connection and inversion coefficients.
reviewed by: W. Koepf
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1326392
zbMATH Keywords: Askey tableau
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: connection problem
zbMATH Keywords: inversion problem
zbMATH Keywords: Charlier polynomials
zbMATH Keywords: Meixner polynomials
zbMATH Keywords: Krawtchouk polynomials
zbMATH Keywords: Hahn polynomials
zbMATH Keywords: Gram polynomials
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Hermite polynomials
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: s0377-0427(98)00167-8
OpenAlex ID: W2047281071
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description: scientific article; zbMATH DE number 1326392