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 ofthe function. This approach is based on contour integration using Cauchy’s formula and Hankel-like contours. 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. Key words, asymptotic analysis, generating functions, combinatorial enumeration AMS(MOS) subject classifications. 05, 40, 68