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Zbl 0712.05004
Flajolet, Philippe; Odlyzko, Andrew
Singularity analysis of generating functions. (English)
[J] SIAM J. Discrete Math. 3, No.2, 216-240 (1990). ISSN 0895-4801; ISSN 1095-7146/e

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.''
[R.C.Read]

MSC 2000:: *05A15 Combinatorial enumeration problems
40E05 Tauberian theorems, general

Keywords: asymptotic analysis; generating functions; combinatorial enumeration; Tauberian theorems

Cited in: Zbl 1229.05028 Zbl 1126.05019 Zbl 1030.60064 Zbl 0982.05011 Zbl 0968.33002 Zbl 0755.05004 Zbl 0978.05531

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