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Asymptotics of Multivariate Sequences: I. Smooth Points of the Singular Variety

✍ Scribed by Robin Pemantle; Mark C. Wilson

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 241 KB
Volume: 97
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3201

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✦ Synopsis

Given a multivariate generating function F(z 1 , ..., z d )=; a r1, ..., rd z r1 1 • • • z rd d , 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 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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