Functional equations and electrostatic models for orthogonal polynomials
type: Item
instance of: scholarly article
zbMATH Open document ID: 1008.42021
publication date: 2003-03-31T00:00:00Z
full work available at URL: Book40
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 1683611
zbMATH Keywords: discriminants
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: zeros
zbMATH Keywords: interacting particles
author: Mourad E. H. Ismail
MaRDI profile type: Publication
title: Functional equations and electrostatic models for orthogonal polynomials
review text: The author has written an interesting survey paper on the connections between orthogonal polynomials, the functional equations they satisfy and some extremal problems. NEWLINENEWLINENEWLINEThe zeros of the orthogonal polynomials arise as solutions to electrostatic problems with respect to a logarithmic potential and there is an intimate connection between the discriminant of the orthogonal polynomial and the coefficients arising in a degree reducing differential recurrence relation of the type NEWLINE\[NEWLINE\frac {d}{dx} p_n(x)=A_n(x)p_{n-1}(x)-B_n(x)p_n(x).NEWLINE\]NEWLINE Also generalizations to other linear degree reducing operators are discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0967.00059].
reviewed by: Marcel G. de Bruin
description: scientific article; zbMATH DE number 1683611