Excitation of radial resonator with annular slot

The problem of the external and internal excitation of a radial resonator with a narrow annular slot, which radiates into a half space is considered. A question is raised about the completeness of a set of functions which describe the fields within the resonator during the excitation only by its alternating outside currents. A method of addition and integration of poorly converging series and integrals is applied. A technique for the strict solution of the electrodynamic problem is presented along with calculations of the fundamental parameters of the antenna: the distribution of voltage along the slot, the radiation pattern, polarizational characteristic, composite conductivity of the radiation, and input resistance.