\[I_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma\left%
(\nu+\frac{1}{2}\right)}\int_{0}^{\pi}e^{\pm z\cos\theta}(\sin\theta)^{2\nu}\,%
\mathrm{d}\theta=\frac{(\frac{1}{2}z)^{\nu}}{\pi^{\frac{1}{2}}\Gamma\left(\nu+%
\frac{1}{2}\right)}\int_{-1}^{1}(1-t^{2})^{\nu-\frac{1}{2}}e^{\pm zt}\,\mathrm%
{d}t,\]