Flajolet, Philippe; Odlyzko, Andrew Singularity analysis of generating functions. (English) Zbl 0712.05004 SIAM J. Discrete Math. 3, No. 2, 216-240 (1990). 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 Cited in 9 ReviewsCited in 263 Documents MSC: 05A15 Exact enumeration problems, generating functions 40E05 Tauberian theorems, general MathOverflow Questions: Recovering information for $\sum_{n \leq x}a(n)$ from $\sum_{n \geq 1}a(n)e^{-nx}$ Keywords:asymptotic analysis; generating functions; combinatorial enumeration; Tauberian theorems PDF BibTeX XML Cite \textit{P. Flajolet} and \textit{A. Odlyzko}, SIAM J. Discrete Math. 3, No. 2, 216--240 (1990; Zbl 0712.05004) Full Text: DOI