{
  "id": "1805.06560",
  "version": "v1",
  "published": "2018-05-17T00:35:37.000Z",
  "updated": "2018-05-17T00:35:37.000Z",
  "title": "Extensions of Ramanujan's reciprocity theorem and the Andrews--Askey integral",
  "authors": [
    "Zhi-Guo Liu"
  ],
  "comment": "24 pages",
  "journal": "Journal of mathematical analysis and applications (419) 2014, Pages 1045--1064",
  "categories": [
    "math.CO",
    "math.CA",
    "math.NT",
    "math.QA"
  ],
  "abstract": "Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of $q$-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. The Andrews--Askey integral is a $q$-integral having four parameters with base $q$. Using the same method we extend the Andrews--Askey integral formula to a $q$-integral formula which has seven parameters with base $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-17T00:35:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "11F27",
      "33D05",
      "33D15",
      "32A05",
      "32A10"
    ],
    "keywords": [
      "jacobis triple product identity",
      "extend ramanujans reciprocity theorem",
      "andrews-askey integral formula",
      "partial differential equations",
      "reciprocity formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}