To the problem of diffraction by a strip. Some properties of the Sohwarzschild's series

The $2D$ problem of diffraction of a plane wave by a strip with ideal boundary conditions is considered. The solution is constructed in the form of diffraction series, i.e., the series over the successive acts of scattering by the edges of the slit. The technique of exact transformations of the diffraction series is proposed. The embedding formula and the ordinary differential equations for the far-field diagram of the field is obtained.