\[M_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(1+2\mu\right)z^{\mu+\frac{1}{2}%
}2^{-2\mu}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}+%
\mu+\kappa\right)}\*\int_{-1}^{1}e^{\frac{1}{2}zt}(1+t)^{\mu-\frac{1}{2}-%
\kappa}(1-t)^{\mu-\frac{1}{2}+\kappa}\,\mathrm{d}t,\]