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Laguerre Polynomials
Definition
The Laguerre polynomials are defined as
\[
\begin{align}
L_n^{(\alpha)}(x) &= \sum_{k=0}^n {n+\alpha \choose n-k} \frac{1}{k!} \left(-x\right)^k\\
&= \frac{(\alpha+1)_n}{n!} {}_1F_1 \left(\left. {-n \atop \alpha+1} \; \right| x \right)
\end{align}
\]
