in the preface to Ref.  [@kow95], such an undertaking represents a formidable challenge because as the variable in an asymptotic series moves about the complex plane or its argument changes, a complete asymptotic expansion experiences significant modification due to the Stokes phenomenon [@sto04]. This means that at particular rays or lines in the complex plane, an asymptotic expansion develops jump discontinuities, which can result in the emergence of an extra asymptotic series in the complete asymptotic expansion. Thus, a complete asymptotic expansion is only uniform over either a sector or a ray in the complex plane, which means in turn that in order to exactify a complete asymptotic expansion over all arguments or phases of the variable in the power series, one requires a deep understanding of the Stokes phenomenon. This understanding entails: (1) being able to determine the locations of all jump discontinuities, and (2) solving the more intricate problem of their quantification when they do occur.

Because of the Stokes phenomenon, it becomes necessary not only to specify a complete asymptotic expansion, but also the range of the argument of the variable in the power series of the expansion. The combination of two such statements are referred to 