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