Our work on analytically continued scattering theory based on the Schrödinger equation is reviewed. We give a brief description of how resonances, here defined as partial wave S-matrix poles, can be calculated as complex eigenvalues to the complex scaled Schrödinger equation. A Mittag-Leffler type expansion is then introduced and it is shown how one can partition a scattering cross section into contributions from isolated S-matrix poles and a background. Computationally this method has proven to be considerably faster than conventional methods. A new, faster and more accurate integration method is used. Examples of detailed previous work as well as current research are given.