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