The aim of this research is to develop a method for expanding the Jost functions as a Taylor-type power series on the complex angular momentum plane. From this method in conjunction with the Watson transformation, we were able to express the scattering amplitude as a sum of the background and pole terms, furthermore, this method propose a way of evaluating, numerically, the pole term. To demonstrate how this method may be applied, we considered the Born approximation. We found out that the developed method improved the Born approximation at large scattering angles. Therefore, this method is useful when the di fferential cross section of the background term fails to converge to that of the exact diff erential cross section at large scattering angles. / Dissertation (MSc)--University of Pretoria, 2016. / National Research Foundation (NRF) / Physics / MSc