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.

MSC codes

  1. 05
  2. 40
  3. 68

Keywords

  1. asymptotic analysis
  2. generating functions
  3. combinatorial enumeration

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Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 216 - 240
ISSN (online): 1095-7146

History

Submitted: 4 April 1988
Accepted: 19 April 1989
Published online: 8 August 2006

MSC codes

  1. 05
  2. 40
  3. 68

Keywords

  1. asymptotic analysis
  2. generating functions
  3. combinatorial enumeration

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