Discrete semi-classical orthogonal polynomials: generalized Meixner
type: Item
instance of: scholarly article
title: Discrete semi-classical orthogonal polynomials: generalized Meixner
zbMATH Open document ID: 0591.42015
DOI: 10.1016/0021-9045(86)90073-0
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The property of quasiorthogonality of the derivative of semi classical orthogonal is extended to the discrete case for the generalized Meixner polynomials. The positive weigth \(\rho\) (x) is solution of the difference equation A(x) \(\rho\) (x\(+1)-B(x) \rho (x)=0\) with A(x) and B(x) polynomials of degree respectively \(\alpha\) and \(\beta\). The situation examined here in (0,\(\infty)\) gives the semi-Meixner case (generalized Meixner) for \(\alpha =\beta\) and would give semi-Charlier when \(\alpha >\beta\). From elementary property of the \(\Gamma\) function it could also be shown that no possibilities exist in \((-\infty,+\infty)\).
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 3948953
zbMATH Keywords: quasiorthogonality
zbMATH Keywords: Meixner polynomials
zbMATH Keywords: positive weigth
author: A. Ronveaux
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90073-0
OpenAlex ID: W2064890686
cites work: Q3712910
cites work: Q3742101
cites work: Q3868092
cites work: Q4157418
cites work: Q4753589
description: scientific article; zbMATH DE number 3948953