Spherical-multipole analysis of electromagnetic and acoustical scattering by a semi-infinite elliptic cone

The spherical-multipole analysis of scalar scattering by an acoustically soft or hard elliptic cone, and of electromagnetic scattering by a perfectly conducting elliptic cone, are presented. The series expansions of the exact solutions are of poor convergence, if both source and field points are far from the cone's tip. A mathematical transformation for the acceleration of convergence-due to Euler-is applied to these expansions, to numerically determine the scattering cross sections of these objects. This powerful method can also be used for the numerical evaluation of diffraction coefficients. The paper contains a review of scientific work concerning scattering by objects with edges, corners, tips, etc.