Interlacing of zeros of orthogonal polynomials under modification of the measure
type: Item
instance of: scholarly article
title: Interlacing of zeros of orthogonal polynomials under modification of the measure
zbMATH Open document ID: 1337.30003
author: Dimitar K. Dimitrov
author: Mourad E. H. Ismail
author: Fernando R. Rafaeli
published in: Journal of Approximation Theory
publication date: 2014-09-10T00:00:00Z
review text: The authors investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure \(d \mu(x)\), supported on the interval \((a,b)\) and the other with respect to the measure \(| x - c |^\tau | x - d |^\gamma d\mu(x)\), where \(c\) and \(d\) are outside \((a,b)\). They prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either \(0<\tau\), \(\gamma\leq 1\) or \(\gamma=0\) and \(0<\tau\leq 2\). This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, the authors obtain further statements on the interlacing of the zeros of Jacobi, Laguerre, Meixner, Hahn, Askey-Wilson orthogonal polynomials.
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 6342396
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: zeros of polynomials
MaRDI profile type: Publication
full work available at URL: j.jat.2013.07.007
OpenAlex ID: W2166097549
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DOI: 10.1016/J.JAT.2013.07.007
description: scientific article; zbMATH DE number 6342396