{
  "id": "math/0402305",
  "version": "v1",
  "published": "2004-02-18T18:35:10.000Z",
  "updated": "2004-02-18T18:35:10.000Z",
  "title": "Rogers-Ramanujan and the Baker-Gammel-Wills (Padé) conjecture",
  "authors": [
    "Doron S. Lubinsky"
  ],
  "comment": "43 pages published version",
  "journal": "Ann. of Math. (2), Vol. 157 (2003), no. 3, 847--889",
  "categories": [
    "math.CA"
  ],
  "abstract": "In 1961, Baker, Gammel and Wills conjectured that for functions $f$ meromorphic in the unit ball, a subsequence of its diagonal Pad\\'{e} approximants converges uniformly in compact subsets of the ball omitting poles of $f$. There is also apparently a cruder version of the conjecture due to Pad\\'{e} himself, going back to the earlier twentieth century. We show here that for carefully chosen $q$ on the unit circle, the Rogers-Ramanujan continued fraction $$1+\\frac{qz|}{|1}+\\frac{q^{2}z|}{|1}+\\frac{q^{3}z|}{|1}+... $$ provides a counterexample to the conjecture. We also highlight some other interesting phenomena displayed by this fraction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-18T18:35:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "baker-gammel-wills",
      "earlier twentieth century",
      "cruder version",
      "approximants converges"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2305L"
    }
  }
}