Sharp bounds for the extreme zeros of classical orthogonal polynomials
type: Item
instance of: scholarly article
title: Sharp bounds for the extreme zeros of classical orthogonal polynomials
zbMATH Open document ID: 1206.33008
author: Dimitar K. Dimitrov
author: G. Nikolov
published in: Journal of Approximation Theory
publication date: 2010-11-18T00:00:00Z
review text: Using the property that the classical orthogonal polynomials satisfy a second order differential equation the authors obtain very sharp bounds for the extreme zeros of the polynomials in question. The numerical tests with Jacobi, Gegenbauer, Laguerre and Hermite polynomials show that the obtained bounds are better than the previously known bounds presented in different papers by Moak, Saff, Varga, Ismail, Li and Krasikov.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 5817261
zbMATH Keywords: classical orthogonal polynomials
zbMATH Keywords: extreme zeros
MaRDI profile type: Publication
full work available at URL: j.jat.2009.11.006
OpenAlex ID: W2164348911
cites work: Zeros of Gegenbauer and Hermite polynomials and connection coefficients
cites work: Some new asymptotic properties for the zeros of Jacobi, Laguerre, and Hermite polynomials
cites work: On a conjecture concerning monotonocity of zeros of ultraspherical polynomials
cites work: Monotonicity of zeros of Jacobi polynomials
cites work: Some recent results on the zeros of Bessel functions and orthogonal polynomials
cites work: On the Derivative with Respect to a Parameter of a Zero of a Sturm–Liouville Function
cites work: Inequalities for real-root polynomials and entire functions
cites work: The variation of zeros of certain orthogonal polynomials
cites work: Q3475560
cites work: Bound on the Extreme Zeros of Orthogonal Polynomials
cites work: A Discrete Approach to Monotonicity of Zeros of Orthogonal Polynomials
cites work: Q3433584
cites work: On the Zeros of Jacobi Polynomials P ( | alpha n , | beta n ) n (X)
cites work: Properties of zeros of orthogonal polynomials and related functions
cites work: Q3508195
cites work: Q4631623
cites work: Zeros of polynomials. Translated from the Bulgarian
cites work: Q4061445
DOI: 10.1016/J.JAT.2009.11.006
description: scientific article; zbMATH DE number 5817261