Singularity analysis of generating functions. (English) Zbl 0712.05004

From the authors’ abstract: “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 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.”
Reviewer: R.C.Read


05A15 Exact enumeration problems, generating functions
40E05 Tauberian theorems
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