Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures
type: Item
instance of: scholarly article
title: Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures
zbMATH Open document ID: 1306.33020
author: Yen Chi Lun
author: Fernando R. Rafaeli
published in: Numerical Algorithms
publication date: 2014-12-16T00:00:00Z
review text: In 2009, \textit{W. Gautschi} [Numer. Algorithms 50, No. 1, 93--96 (2009; Zbl 1165.33009); ibid. 50, No. 3, 293--296 (2009; Zbl 1168.33001)] conjectured two inequalities for the zeros \(x_{n,k}^{(a,b)}\), \(k=1,2,\ldots,n\) of Jacobi polynomials and especially for \(\theta_{n,k}^{(a,b)}=\arccos x_{n,k}^{(a,b)}\). The authors establish the conjectures for large domains of the \((a,b)\) plane. Their main tool is Sturm's comparison theorem for the zeros of solutions of the Sturm-Liouville differential equation. Especially they present a direct consequence of Sturm's theorem and they analyze a particular function that appears in the proof of the theorem.
reviewed by: Chrysoula G. Kokologiannaki
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6380840
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: zeros
zbMATH Keywords: inequalities
zbMATH Keywords: Gautschi's conjectures
zbMATH Keywords: Sturm's theorem
describes a project that uses: CIZJP
MaRDI profile type: Publication
full work available at URL: s11075-013-9807-7
OpenAlex ID: W2074986700
Wikidata QID: Q122889306
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DOI: 10.1007/S11075-013-9807-7
description: scientific article; zbMATH DE number 6380840