{
  "id": "2203.16047",
  "version": "v1",
  "published": "2022-03-30T04:29:08.000Z",
  "updated": "2022-03-30T04:29:08.000Z",
  "title": "$q$-Rational Reduction and $q$-Analogues of Series for $π$",
  "authors": [
    "Rong-Hua Wang",
    "Michael X. X. Zhong"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper, we present a $q$-analogue of the polynomial reduction which was originally developed for hypergeometric terms. Using the $q$-Gosper representation, we describe the structure of rational functions that are summable when multiplied with a given $q$-hypergeometric term. The structure theorem enables us to generalize the $q$-polynomail reduction to the rational case, which can be used in the automatic proof and discovery of $q$-identities. As applications, several $q$-analogues of series for $\\pi$ are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-30T04:29:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A10",
      "11B65"
    ],
    "keywords": [
      "rational reduction",
      "hypergeometric term",
      "structure theorem enables",
      "polynomial reduction",
      "polynomail reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}