An Orthogonality Property of the Legendre Polynomials

2015/05/25 by Bos, Len, Narayan, Akil, Levenberg, Norm +1
#33C45 #41A10 #65C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.06635

Abstract

We give a remarkable additional orthogonality 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 degree-n normalized Christoffel function.

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