A review of a recursive algorithm with a more succinct derivation is first presented. This algorithm, which calculates the scattering solution from an inhomogeneous body, first divides the body into N subscatterers. The algorithm then uses an aggregate T matrix and translation formulas to solve for the solution of n+1 subscatterers from the solution for n subscatterers. This recursive algorithm has reduced computational complexity. Moreover, the memory requirement is proportional to the number of unknowns. This algorithm has been used successfully to solve for the volume scattering solution of two-dimensional scatterers for Ez-polarized waves. However, for Hz-polarized waves, a straightforward application of the recursive algorithm yields unsatisfactory solutions due to the violation of the restricted regime of the addition theorem. But by windowing the addition theorem, the restricted regime of validity is extended. Consequently, the recursive algorithm with the windowed addition theorem works well even for Hz-polarized waves.