Singularity Analysis of Generating Functions.

This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic expansion for the Taylor coefficients of the function. This approach is based on contour integration a la Hankel and Cauchy's formula. It constitutes an alternative to either Darboux's method or Tauberian theorems that appears to be well suited to combinatorial enumerations and a few applications in this area are outlined.