\[\mathbf{M}_{\nu}\left(z\right)=-\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\Gamma%
\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{1}e^{-zt}(1-t^{2})^{\nu-\frac{1}{2}}\,%
\mathrm{d}t,\]