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We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials Pₘ and Pₙ of orders m and n, respectively, we provide simple derivations of the integrals ₀¹ Pₙ (2x-1) Pₘ (2x-1) (x) dx.
Sebastian Schmutzhard-Höfler (Wed,) studied this question.