{
  "id": "math/0606781",
  "version": "v1",
  "published": "2006-06-30T06:19:11.000Z",
  "updated": "2006-06-30T06:19:11.000Z",
  "title": "On A Relation Between $q$-Exponential And $θ$-Function",
  "authors": [
    "Ruiming Zhang"
  ],
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We will use a discrete analogue of the classical Laplace method to show that for infinitely many positive integers $n$, the main term of the asymptotic expansion of the scaled $q$-exponential $(-q^{-nt+1/2}u;q)_{\\infty}$ could be expressed in $\\theta$-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-30T06:19:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45",
      "33E05"
    ],
    "keywords": [
      "exponential",
      "asymptotic expansion",
      "discrete analogue",
      "main term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6781Z"
    }
  }
}