Asymptotics of multivariate sequences: I. Smooth points of the singular variety

Authors:
Robin Pemantle;Mark C. Wilson
Affiliations:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio;Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, Ohio
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 9
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Abstract

Given a multivariate generating function F(z1, ...,zd) = Σ ar1, ...,rd z1r1 ...zdrd, 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.