Corpus ID: 2805773

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

@article{Pemantle2000AsymptoticsOM,
  title={Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety},
  author={R. Pemantle and M. Wilson},
  journal={arXiv: Combinatorics},
  year={2000}
}
  • R. Pemantle, M. Wilson
  • Published 2000
  • Mathematics
  • arXiv: Combinatorics
  • 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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