\[J_{\nu}\left(x\right)=\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\Gamma%
\left(-t\right)(\tfrac{1}{2}x)^{\nu+2t}}{\Gamma\left(\nu+t+1\right)}\,\mathrm{%
d}t,\]