Laplaceʹs method on a computer algebra system with an application to the real valued modified Bessel functions

We examine a Maple implementation of two distinct approaches to Laplaceʹs method used to obtain asymptotic expansions of Laplace-type integrals. One algorithm uses power series reversion, whereas the other expands all quantities in Taylor or Puiseux series. These algorithms are used to derive asymptotic expansions for the real valued modified Bessel functions of pure imaginary order and real argument that mimic the well-known corresponding expansions for the unmodified Bessel functions.