\[f(x)=\int_{0}^{\infty}(xt)^{\frac{1}{2}}\frac{J_{\nu}\left(xt\right)Y_{\nu}%
\left(at\right)-Y_{\nu}\left(xt\right)J_{\nu}\left(at\right)}{{J_{\nu}}^{2}%
\left(at\right)+{Y_{\nu}}^{2}\left(at\right)}\*\int_{a}^{\infty}(yt)^{\frac{1}%
{2}}\left(J_{\nu}\left(yt\right)Y_{\nu}\left(at\right)-Y_{\nu}\left(yt\right)J%
_{\nu}\left(at\right)\right)f(y)\,\mathrm{d}y\,\mathrm{d}t,\]