Use Of The Zonal Harmonic Series For Obtaining Numerical Solutions To Electromagnetic Boundary Value Problems

This is a discussion of the application of the zonal harmonic series to problems involving dipole sources in the vicinity of spherical boundaries. The application of a formal zonal-harmonic series solution to directly obtain numerical results involves two distinct problems: namely, the convergence of the series solution and the accurate calculation of the special functions involved in the series solution. Some interesting techniques will be introduced which help to improve the convergence properties of the series solution.