Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice \(x(s)=q^{2s}\)
type: Item
instance of: scholarly article
title: Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice \(x(s)=q^{2s}\)
zbMATH Open document ID: 0933.33012
DOI: 10.1016/S0377-0427(98)00162-9
author: Stanisław Lewanowicz
published in: Journal of Computational and Applied Mathematics
publication date: 1999-08-22T00:00:00Z
review text: Let \(\{P_k(x)\}\) be any system of classical orthogonal polynomials of a discrete variable such that \[ \sum^{B-1}_0 P_k(x(s)) P_\ell(x(s)) \ell(s)\Delta x(s-1/2)= \delta_{k\ell} d^2_k \] and also \(\overline P_n= \sum^n_0 C_{nk}P_k\), where \(\overline P_n\) is another family of similar polynomials and \(C_{nk}\) are connection coefficients. In this paper the recurrence relations satisfied by the connection coefficient in terms of the coefficients \(\sigma\) and \(\tau\) of the Pearson equation, have been obtained.
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 33E30
zbMATH DE Number: 1326373
zbMATH Keywords: classical orthogonal polynomials
reviewed by: B. M. Agrawal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326373