Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety

Details Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety

2000-03-28

arxiv.org/abs/math/0003192v1

Mathematics

Combinatorics

23 pages, 2 figures

Scientific paper

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.

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