\[\int_{0}^{\infty}J_{\nu}\left(at\right)J_{\nu}\left(bt\right)\frac{t\,\mathrm{%
d}t}{t^{2}-z^{2}}=\left\{\begin{array}[]{ll}\frac{1}{2}\pi iJ_{\nu}\left(bz%
\right){H^{(1)}_{\nu}}\left(az\right),&a>b\\
\frac{1}{2}\pi iJ_{\nu}\left(az\right){H^{(1)}_{\nu}}\left(bz\right),&b>a\end{%
array}\right\},\]