\[\int z^{-\nu}\mathbf{L}_{\nu+1}\left(z\right)\,\mathrm{d}z=z^{-\nu}\mathbf{L}_%
{\nu}\left(z\right)-\frac{2^{-\nu}z}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}%
\right)}.\]