Transient and time-harmonic diffraction by a semi-infinite cone

New representations for the time-dependent scalar Green's functions for a perfectly conducting semi-infinite cone are derived. When the cone angle is small and the source is located on the cone axis, the solutions for all observation times can be expressed in remarkably simple closed forms involving only elementary functions. New elementary time-harmonic Green's function approximations, valid for all frequencies, are then obtained from Fourier inversion of the closed form transient results.