\[\frac{1}{\pi}\int_{0}^{2\pi}\cos\left(\nu\theta-z\sin\theta\right)\,\mathrm{d}%
\theta=(1+\cos\left(2\pi\nu\right))\,\mathbf{J}_{\nu}\left(z\right)+\sin\left(%
2\pi\nu\right)\mathbf{E}_{\nu}\left(z\right).\]