An Orthogonality Property of the Legendre Polynomials

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• 作者：L. Bos ; A. Narayan ; N. Levenberg ; F. Piazzon
• 关键词：Legendre polynomials ; Christoffel function ; Equilibrium measure
• 刊名：Constructive Approximation
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：45
• 期：1
• 页码：65-81
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Analysis;
• 出版者：Springer US
• ISSN：1432-0940
• 卷排序：45

文摘

We give a remarkable additional othogonality property of the classical Legendre polynomials on the real interval \([-1,1]\): polynomials up to degree n from this family are mutually orthogonal under the arcsine measure weighted by the normalized degree-n Christoffel function.