English

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

Combinatorics 2007-05-23 v1 Probability

Abstract

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.

Keywords

Cite

@article{arxiv.math/0003192,
  title  = {Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety},
  author = {R. Pemantle and M. C. Wilson},
  journal= {arXiv preprint arXiv:math/0003192},
  year   = {2007}
}

Comments

23 pages, 2 figures