\[J_{n}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}\cos\left(z\sin\theta-n\theta%
\right)\,\mathrm{d}\theta=\frac{i^{-n}}{\pi}\int_{0}^{\pi}e^{iz\cos\theta}\cos%
\left(n\theta\right)\,\mathrm{d}\theta,\]