Scalar wave scattering of a prolate spheroid as a parameter expansion of that of a sphere

Abstract

In this paper the scattering problem for the prolate spheroid, \[ Δ U p + k 2 U p = 0 \Delta {U_p} + {k^2}{U_p} = 0 \] , is solved by way of an asymptotic parameter expansion, where the spheroid is considered a perturbation of a sphere (which has an exact solution). The error of the asymptotic approximation is then estimated.