Rodrigues' formula
= Rodrigues' formula
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A Rodrigues formula constructs an <orthogonal polynomial> by differentiating a weight multiplied by a power. The <Rodrigues formula for Legendre polynomials> uses a derivative of $(x^2-1)^l$. For <Generalized Laguerre polynomials>,
$$
L_n^{(\alpha)}(x)
=\frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}
\left(e^{-x}x^{n+\alpha}\right).
$$