On the zeros of orthogonal polynomials: the elliptic case
type: Item
instance of: scholarly article
title: On the zeros of orthogonal polynomials: the elliptic case
zbMATH Open document ID: 1056.42020
author: Franz Peherstorfer
published in: Constructive Approximation
publication date: 2004-10-28T00:00:00Z
review text: Let \(E=[-1,\alpha]\cup[\beta,1],\;-1<\alpha<\beta<1,\) and let \((p_n)\) be orthogonal on \(E\) with respect to the weight function \(((1-x^2)(x-\alpha)(x-\beta))^{\pm 1/2}/W(x),\) where \(W\) is positive on \(E\) and \(W\in C^3(E).\) The author gives the exact number (in terms of elliptic functions) of zeros of \(p_n\) in the two intervals and in the gap \((\alpha,\beta).\) Also, the accumulation points of the zeros are completely described and corresponding results are proved if \(W\) has a different sign on two intervals of \(E.\)
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 2111591
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: number of zeros
zbMATH Keywords: elliptic functions
zbMATH Keywords: two intervals
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: s00365-004-0566-5
OpenAlex ID: W2081258777
DOI: 10.1007/S00365-004-0566-5
description: scientific article; zbMATH DE number 2111591