\[\mathbf{L}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\Gamma%
\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\pi/2}\sinh\left(z\cos\theta\right)(%
\sin\theta)^{2\nu}\,\mathrm{d}\theta,\]