Solve this integral equation: $$ {{\rm e}^{{\rm i}k\,\sqrt{\vphantom{\Large A}\,r^{2} + z^{2}\,}\,} \over \sqrt{\vphantom{\large A}r^{2} + z^{2}\,}} = \int_0^{\infty}{\rm K}_{0}\left(\lambda r\right) \cos\left(\,\sqrt{\vphantom{\Large A}\,\lambda^{2} + k^{2}\,}\,z\right) {\rm f}\left(\lambda\right)\,{\rm d}\lambda $$
where ${\rm f}\left(\lambda\right)$ is the unknown function. ${\rm K}_{0}\left(\lambda r\right)$ is the modified Bessel function of the second kind of order zero. $r > 0$.
Could anyone give some hints ?. Thanks !.