\[\int_{0}^{\infty}{\mathrm{e}}^{-x}x^{\alpha}L^{(\alpha)}_{n}\left(x\right){%
\mathrm{e}}^{\mathrm{i}xy}\,\mathrm{d}x=\frac{\Gamma\left(\alpha+n+1\right)(-%
\mathrm{i}y)^{n}}{n!\left(1-\mathrm{i}y\right)^{\alpha+n+1}},\]