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

Given a multivariate generating function F(z1, ?, zd)=?ar1, ?, rdzr11?zrdd, 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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