Orthogonality of polar Legendre polynomials and approximation

2025/06/05 by Abdelhamid Rehouma, Rehouma, Abdelhamid
Mathematics · #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2506.04918

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Q_n(x)\ be a system of integral Legendre polynomials of degree exactly n,and let \P_n(x)\ be polar polynomials primitives of integral Legendre polynomials. We derive some identities and relations and extremal problems and minimization involving of polar integral Legendre polynomials.

Citations

• On Polar Legendre Polynomials

Related

• Integrals of Legendre polynomials and approximations
• On Polar Legendre Polynomials
• An Orthogonality Property of the Legendre Polynomials
• Lecture notes on Legendre polynomials: their origin and main properties
• An improved bound on Legendre approximation