ABSTRACT
This chapter considers dual series equations with kernels that are asymptotically similar to Jacobi polynomials. It focuses on prolate spheroidal shells. The chapter examines axially symmetric magnetic dipole excitation of the same cavity that gives rise to a boundary value problem for the azimuthal component of electric field Eϕ. It deals with a more complicated structure, the closed prolate spheroid embedded in a spheroidal cavity. The solution is employed to analyse the resonant properties of the shielded dipole antenna. The chapter considers the scalar wave problem for the prolate spheroidal shell with one circular hole; the infinitely thin, acoustically hard spheroidal screen is excited by plane acoustic wave normally incident on the aperture plane. It analyses the regularised system to develop a rigorous theory of the spheroidal Helmholtz resonator. The chapter considers the excitation of the spheroidal cavity with a single circular aperture by a magnetic dipole.
