An algebraic formula for the accelerated computation of the low frequency scattering coefficients: The case of the acoustically soft sphere

An explicit expression for the rapid computation of the low frequency scattering coefficients is presented. Although the demonstration of the methodology is restricted to the simple case of an acoustically soft spherical scatterer, the introduced main concept can be applied to a wide class of scattering problems. The procedure, based on algebraic calculations only, provides an analytic expression of the corresponding scattering coefficients in a straightforward fashion. The proposed algorithm is readily implemented, furnishing an efficient way for obtaining any order approximation of the total field in the exterior of the scatterer.