{
  "id": "1210.2493",
  "version": "v2",
  "published": "2012-10-09T04:32:57.000Z",
  "updated": "2012-12-04T10:35:59.000Z",
  "title": "A generating function of the squares of Legendre polynomials",
  "authors": [
    "Wadim Zudilin"
  ],
  "comment": "7 pages",
  "journal": "Bull. Austral. Math. Soc. 89:1 (2014) 125--131",
  "doi": "10.1017/S0004972713000233",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP",
    "math.NT"
  ],
  "abstract": "We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we resolve a subfamily of identities involving $1/\\pi$ which was experimentally observed by Zhi-Wei Sun.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-04T10:35:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "11F03",
      "11F11",
      "11Y60",
      "33C45"
    ],
    "keywords": [
      "legendre polynomials",
      "arithmetic hypergeometric series",
      "modular parametrisation",
      "one-parametric generating function",
      "shaun cooper"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2493Z"
    }
  }
}