  The study of asymptotic properties of solutions to differential equations has
a long and arduous history, with the most significant advances having been made
in the development of quantum mechanics. A very powerful method of analysis is
that of Phase Integrals, described by Heading. Key to this analysis are the
Stokes constants and the rules for analytic continuation of an asymptotic
solution through the complex plane. These constants are easily determined for
isolated singular points, by analytically continuing around them and, in the
case of analytic functions, requiring the asymptotic solution to be single
valued. However, most interesting problems of mathematical physics involve
several singular points. By examination of analytically tractable problems and
more complex bound state problems involving multiple singular points, we show
that the method of Phase Integrals can greatly improve the determination of
bound state energies over the simple WKB values. We also find from these
examples that in the limit of large separation the Stokes constant for a first
order singular point approaches the isolated singular point value.
