On calculation of some integrals, describing the wave fields

Two methods of calculation of scattering amplitude $f(\omega,\omega_0)$ of the wave scattered by the vertex of an arbitrarily shaped cone are justified. It is shown that the approximation $f_d(\omega,\omega_0,t)$, obtained by the method similar to Abel–Poisson's method of summation, converges uniformly in the domain of regularity of $f$. Also the possibility of calculation of $f(\omega,\omega_0)$ when $\omega\in N_1(\omega_0)$ by means of rapidly converging integrals is proved.