2000/03/28 by Robin Pemantle, R. Pemantle, Mark C. Wilson +3
Computer Science · Mathematics · #05A16 (Primary) #32A20 #41A60 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Mathematics and Applications #Polynomial and algebraic computation #Probability (math.PR) #math.CO #math.PR #msc:05A16 #msc:32A20 #msc:41A60
paper · pdf · doi:10.48550/arxiv.math/0003192
23 pages, 2 figures
arxiv created 2000/03/28 · openalex publication_date 2000/03/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a multivariate generating function F, we determine asymptotics for the coefficients. Our approach is to use Cauchy's integral formula near singular points of F, resulting in a tractable oscillating integral. This paper treats the case where the singular point of F is a smooth point of a surface of poles. Companion papers will treat singular points of F where the local geometry is more complicated, and for which other methods of analysis are not known.