A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight

2024/04/17 by Schmutzhard-Höfler, Sebastian
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.11173

Abstract

We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials P_m and P_n of orders m and n, respectively, we provide simple derivations of the integrals ∫ ₀¹ P_n(2x-1) P_m(2x-1)log (x)dx.

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