\[J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=\frac{1}{2\pi i}\int_{c-i\infty%
}^{c+i\infty}\*\exp\left(\frac{1}{2}t-\frac{z^{2}+\zeta^{2}}{2t}\right)I_{\nu}%
\left(\frac{z\zeta}{t}\right)\frac{\,\mathrm{d}t}{t},\]