\[L^{(\alpha)}_{n}\left(x\right)=\sum_{\ell=0}^{n}\frac{{\left(\alpha+\ell+1%
\right)_{n-\ell}}}{(n-\ell)!\;\ell!}(-x)^{\ell}=\frac{{\left(\alpha+1\right)_{%
n}}}{n!}{{}_{1}F_{1}}\left({-n\atop\alpha+1};x\right).\]