Orthogonality of Legendre polynomials (source code)

= Orthogonality of Legendre polynomials
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The Legendre polynomials are orthogonal on $[-1,1]$ with unit weight:
$$
\int_{-1}^1P_\ell(x)P_m(x)\,dx
=\frac{2}{2\ell+1}\delta_{\ell m}.
$$