Recently, was developed a new theory of the Jost function, within which, it was split in two terms involving on one side, singlevalued analytic functions of the energy, and on the other, factors responsible for the existence of the branching-points. For the single-valued part of the Jost function, a procedure for the powerseries expansion around an arbitrary point on the energy plane was suggested. However, this theory lacks a rigorous proof that these parts are entire functions of the energy. It also gives an intuitive (not rigorous) derivation of the domain where they are entire. In the present study, we ll this gap by using a method derived from the method of successive approximations. / Dissertation (MSc)--University of Pretoria, 2013. / gm2014 / Physics / unrestricted