An Orthogonality Property of the Legendre Polynomials

被引：2

作者：

Bos, L. ^{[1
]}

Narayan, A. ^{[2
]}

Levenberg, N. ^{[3
]}

Piazzon, F. ^{[4
]}

机构：

[1] Univ Verona, Dept Comp Sci, Verona, Italy

[2] Univ Utah, Dept Math, Sci Comp & Imaging Inst SCI, Salt Lake City, UT 84112 USA

[3] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[4] Univ Padua, Dept Math, Padua, Italy

来源：

CONSTRUCTIVE APPROXIMATION | 2017年 / 45卷 / 01期

基金：

美国国家科学基金会;

关键词：

Legendre polynomials; Christoffel function; Equilibrium measure;

D O I：

10.1007/s00365-015-9321-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：65 / 81

页数：17

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