composed of divergent series, exactification involves being able to obtain meaningful values from such series. To evaluate these, one must introduce the concept of regularization, which is defined in this work as the removal of the infinity in the remainder of an asymptotic series in order to make the series summable. It was first demonstrated in Ref. [@kow001] that the infinity appearing in the remainder of an asymptotic series arises from an impropriety in the method used to derive it. Consequently, regularization was seen as a necessary means of correcting an asymptotic method such as the method of steepest descent or iteration of a differential equation. Regularization was also shown to be analogous to taking the finite or Hadamard part of a divergent integral [@kow001]- [@kow11c].

Two very different techniques will be used to regularize the divergent series appearing throughout this work. As described in Refs. [@kow002; @kow09], the most common method of regularizing a divergent series is Borel summation, but often, it produces results that are not amenable to fast and accurate computation. To overcome this drawback, the numerical technique of Mellin-Barnes regularization was developed for the first time in Ref. [@kow95]. In this regularization technique divergent series are 