\[(\tfrac{1}{2}z)^{-\nu-1}\mathbf{L}_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{%
\infty}^{(0+)}\frac{\pi\csc\left(\pi s\right)}{\Gamma\left(\tfrac{3}{2}+s%
\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right)}(-\tfrac{1}{4}z^{2})^{s}\,\mathrm%
{d}s.\]