{
  "id": "0906.4290",
  "version": "v3",
  "published": "2009-06-23T16:00:40.000Z",
  "updated": "2010-01-13T10:58:35.000Z",
  "title": "Asymptotics of partial sums of central binomial coefficients and Catalan numbers",
  "authors": [
    "Sandro Mattarei"
  ],
  "comment": "8 pages; a new section has been added, about congruences modulo a prime",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove exact asymptotic expansions for the partial sums of the sequences of central binomial coefficients and Catalan numbers, $\\sum_{k=0}^n \\binom{2k}{k}$ and $\\sum_{k=0}^n C_n$. We also obtain closed forms for the polynomials $\\sum_{k=0}^{q-1}\\binom{2k}{k}x^k$ and $\\sum_{k=0}^{q-1}C_kx^k$ over the field of $p$ elements, where $q$ is a power of the prime $p$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-13T10:58:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05A10"
    ],
    "keywords": [
      "central binomial coefficients",
      "catalan numbers",
      "partial sums",
      "exact asymptotic expansions",
      "closed forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4290M"
    }
  }
}