{
  "id": "math/0003192",
  "version": "v1",
  "published": "2000-03-28T19:27:22.000Z",
  "updated": "2000-03-28T19:27:22.000Z",
  "title": "Asymptotics of Multivariate Sequences, part I. Smooth points of the singular variety",
  "authors": [
    "R. Pemantle",
    "M. C. Wilson"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-28T19:27:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "32A20",
      "41A60"
    ],
    "keywords": [
      "smooth point",
      "singular variety",
      "multivariate sequences",
      "treat singular points",
      "cauchys integral formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3192P"
    }
  }
}