The variation of zeros of certain orthogonal polynomials
type: Item
instance of: scholarly article
title: The variation of zeros of certain orthogonal polynomials
zbMATH Open document ID: 0628.33001
DOI: 10.1016/0196-8858(87)90009-1
author: Mourad E. H. Ismail
published in: Advances in Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author considers certain orthogonal polynomial systems defined by a three-term recurrence relation in which the coefficients are functions of a parameter \(\nu\), and seeks conditions for the largest and smallest zeros of these polynomials to be monotone functions of \(\nu\). A typical result is that the largest zero of a birth-death polynomial increases (decreases) with \(\nu\) if the birth and death rates are increasing (decreasing) functions of \(\nu\). Related results are obtained for random walk polynomials and a class of polynomials which includes the Lommel polynomials. The proofs use a finite-dimensional version of the Hellman- Feynman theorem.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4021605
zbMATH Keywords: birth-death polynomial
zbMATH Keywords: random walk polynomials
zbMATH Keywords: Lommel polynomials
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
full work available at URL: 0196-8858(87)90009-1
OpenAlex ID: W2066213190
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description: scientific article; zbMATH DE number 4021605