Sebastian Schmutzhard-Höfler
Published 2024-04-17Version 1
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 $$\int \limits_0^1 P_n(2x-1) P_m(2x-1)\log (x)dx.$$
Szegö kernels and asymptotic expansions for Legendre polynomials
A generating function of the squares of Legendre polynomials
Recurrence coefficients for orthogonal polynomials with a logarithmic weight function
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