A property of the zeros of the Legendre polynomials
type: Item
instance of: scholarly article
title: A property of the zeros of the Legendre polynomials
zbMATH Open document ID: 0658.42025
DOI: 10.1016/0021-9045(87)90068-2
author: C. C. Grosjean
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: By applying Sturm's comparison theorem, the author proves that the zeros of the Legendre polynomials \(P_ n(x)\) satisfy the following elegant inequality: \((1-x^{(n)}_{j-1})(1-x^{(n)}_{j+1})<(1-x_ j^{(n)})^ 2,\) true for all \(j\in \{2,3,...,(n-1)\}\) and \(n\in \{3,4,...\}\).
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 4075754
zbMATH Keywords: Sturm's comparison theorem
zbMATH Keywords: Legendre polynomials
reviewed by: Ajendra Nath Srivastava
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90068-2
OpenAlex ID: W1998713743
cites work: On the Spacing of the Zeros of Some Classical Orthogonal Polynomials
cites work: Higher monotonicity properties of certain Sturm-Liouville functions
cites work: Q5720308
cites work: Higher Monotonicity Properties of Certain Sturm-Liouville Functions. III
cites work: Higher Monotonicity Properties of Certain Sturm-Liouville Functions. IV
description: scientific article; zbMATH DE number 4075754