{
  "id": "math/0611211",
  "version": "v1",
  "published": "2006-11-08T03:32:00.000Z",
  "updated": "2006-11-08T03:32:00.000Z",
  "title": "On The Chaotic Asymptotics of Ramanujan's Entire Function $A_q(z)$",
  "authors": [
    "Ruiming Zhang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We will use a discrete analogue of the classical \\emph{Laplace} method to show that for infinitely many positive integers $n$, the main term of the asymptotic expansions of scaled confluent basic hypergeometric functions, including the Ramanujan's entire function $A_{q}(z)$, could be expressed in $\\theta$-functions, and the error term depends on the ergodic property of certain real scaling parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-08T03:32:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45",
      "33E05"
    ],
    "keywords": [
      "ramanujans entire function",
      "chaotic asymptotics",
      "scaled confluent basic hypergeometric functions",
      "error term depends",
      "asymptotic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11211Z"
    }
  }
}