\[\int_{0}^{\infty}{\mathrm{e}}^{-ax}L^{(\alpha)}_{n}\left(bx\right)x^{z-1}\,%
\mathrm{d}x=\frac{\Gamma\left(z+n\right)}{n!}\*{(a-b)^{n}}a^{-n-z}\*{{}_{2}F_{%
1}}\left({-n,1+\alpha-z\atop 1-n-z};\frac{a}{a-b}\right),\]