[[Special functions MOC]]
# Laguerre polynomial

The $p$th Laguerre polynomial $L_{q}$ for $q \in \mathbb{N}_{0}$ is a polynomial of degree $p$ given by #m/def/fun
$$
\begin{align*}
L_{q}(x) = \frac{e^x}{q!} \left( \frac{d}{dx} \right)^q (e^{-x}x^q)
\end{align*}
$$

> [!code] Mathematica
> The Laguerre polynomial $L_{p}(x)$ may be generated in [[Wolfram Mathematica]] with `LaguerreL[p,x]`.


[^2018]: 2018\. [[Sources/@griffithsIntroductionQuantumMechanics2018|Introduction to quantum mechanics]], §4.2, p. 150
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