Diffraction series on a sphere and conical asymptotics

The problem of finding field components for a conical diffraction problem is studied. All components except the spherical wave diffracted by cone tip are under consideration. As a starting point, the integral formula (7) derived by Babich et al. is used. A geometrical optics approximation of the spherical Green's function is constructed in the form of diffraction series. There is a finite set of terms of the diffraction series on sphere, to each of which the conical field components correspond. Formula (7) is simplified, giving a convenient field representation (26). In many cases further simplification can be performed, giving formula (30) directly converting the terms of the diffraction series on sphere into the field component in the 3D space.