\[\lim_{R\to\infty}\int_{0}^{\infty}f(y)\left(\int_{0}^{R}\sqrt{xt}J_{\nu}\left(%
xt\right)\sqrt{yt}J_{\nu}\left(yt\right)\,\mathrm{d}t\right)\,\mathrm{d}y=%
\tfrac{1}{2}\left(f(x+)+f(x-)\right),\]