On an integral equation in the problem of the plane wave diffraction by a circular transparent cone

The problem of diffraction by a transparent convex cone is studied. The uniqueness theorem is proven in the problem of diffraction for the illumination by a compact source. For the circular cone the solution is obtained in the form of the Kontorovich–Lebedev integrals and of the Fourier series expansions. A singular integral equation is deduced for the Fourier coefficients and its reqularization is performed.