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