\[f(x)=\int_{0}^{\infty}(xt)^{\frac{1}{2}}\frac{cJ_{\nu}\left(xt\right)+t^{2\nu}%
J_{-\nu}\left(xt\right)}{c^{2}+2c\cos\left(\nu\pi\right)t^{2\nu}+t^{4\nu}}\*%
\int_{0}^{\infty}(yt)^{\frac{1}{2}}\left(cJ_{\nu}\left(yt\right)+t^{2\nu}J_{-%
\nu}\left(yt\right)\right)f(y)\,\mathrm{d}y\,\mathrm{d}t,\]