{
  "id": "math/0110238",
  "version": "v3",
  "published": "2001-10-22T10:28:18.000Z",
  "updated": "2002-10-10T14:14:30.000Z",
  "title": "Some new formulas for $π$",
  "authors": [
    "Gert Almkvist",
    "Christian Krattenthaler",
    "Joakim Petersson"
  ],
  "comment": "28 pages, LaTeX; some important references added",
  "journal": "Experiment. Math. 12 (2003), 441-456.",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We show how to find series expansions for $\\pi$ of the form $\\pi=\\sum_{n=0}^\\infty {S(n)}\\big/{\\binom{mn}{pn}a^n}$, where S(n) is some polynomial in $n$ (depending on $m,p,a$). We prove that there exist such expansions for $m=8k$, $p=4k$, $a=(-4)^k$, for any $k$, and give explicit examples for such expansions for small values of $m$, $p$ and $a$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-10-10T14:14:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A25",
      "11B65",
      "11Y60",
      "65B10"
    ],
    "keywords": [
      "series expansions",
      "explicit examples",
      "small values"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10238A"
    }
  }
}