An electrostatics model for zeros of general orthogonal polynomials
type: Item
instance of: scholarly article
title: An electrostatics model for zeros of general orthogonal polynomials
zbMATH Open document ID: 1011.33011
author: Mourad E. H. Ismail
published in: Pacific Journal of Mathematics
publication date: 2000-12-03T00:00:00Z
review text: The author extends the Stieltjes models from Jacobi orthogonal polynomials to general orthogonal polynomials satisfying integrability conditions on their weight functions. It was proved that the zeros of general orthogonal polynomials determine the equilibrium position of movable n unit charges in an external field determined by the weight function. The total energy of the system was computed in terms of the recursion coefficients of the orthogonal polynomials. The limiting behavior as the number of particles tending to infinity was studied in the case of Freud exponential weights.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 78A30
zbMATH DE Number: 1537811
zbMATH Keywords: general orthogonal polynomials
zbMATH Keywords: zeros
zbMATH Keywords: electrostatics model
reviewed by: Matthew He
MaRDI profile type: Publication
full work available at URL: pjm.2000.193.355
OpenAlex ID: W1994084361
DOI: 10.2140/PJM.2000.193.355
description: scientific article; zbMATH DE number 1537811