\[W_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)=(-1)^{n}{%
\left(\alpha+1\right)_{n}}M_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}\alpha%
}\left(z\right)=(-1)^{n}n!e^{-\frac{1}{2}z}z^{\frac{1}{2}\alpha+\frac{1}{2}}L^%
{(\alpha)}_{n}\left(z\right).\]