On a System of p‐Tuple Series Equations Related to the Scattering by an Inhomogeneous Sphere

Abstract

A system of p‐tuple series equations, involving associate Legendre functions, related to the scattering of electromagnetic waves by a spherical surface divided into p parallel strips with different impedances is studied. The original problem of solving a system composed of two p‐tuple series equations is reduced to a problem of solving 2(2p—1) (or two) completely independent p‐tuple series equations with the same kernel as well as a system of linear algebraic equations. The solutions to the independent series equations can be found by successive iterations. The conditions wich guarantee the convergence of the iterations and the uniqueness of the solution are given in two theorems. The results are applied to a simple illustrative example.