Scattering of a highfrequency wave by the vertex of an arbitrary cone. (Singular directions.)

A new approach to the obtaining of the analytical expression for the wave scattered by an arbitrary cone vertex in the singular directions is considered. The spherical front of the wave, propagating from the vertex of the cone tangents the front of the wave, reflected by the cone surface in this “singular” directions. The wave field is expressed in the terms of the parabolic cylinder functions.