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

Sebastian Schmutzhard-Höfler

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arXiv · 2404.11173

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

Sebastian Schmutzhard-Höfler

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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 $$\int \limits_0^1 P_n(2x-1) P_m(2x-1)\log (x)dx.$$

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Sebastian Schmutzhard-Höfler. 2024-04-17. A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight. https://arxiv.org/abs/2404.11173

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