Diffraction by a narrow circular cone as by a strongly elongated body

Leading order terms of the asymptotic expansions in the problems of acoustic and electromagnetic waves diffraction by narrow circular cone are constructed in this paper. By analogy with problems of diffraction by strongly elongated bodies the derivations are carried out in special system of coordinates related to the surface which takes into account that the cone angle is small. Graphics of special functions appearing in the considered problems of diffraction are presented.