{
  "id": "0708.2771",
  "version": "v1",
  "published": "2007-08-21T08:09:04.000Z",
  "updated": "2007-08-21T08:09:04.000Z",
  "title": "Approximations to Euler's constant",
  "authors": [
    "Kh. Hessami Pilehrood",
    "T. Hessami Pilehrood"
  ],
  "comment": "11 pages",
  "journal": "Math. Inequal. Appl. 13 (2010), no. 4, 761--773",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study a problem of finding good approximations to Euler's constant $\\gamma=\\lim_{n\\to\\infty}S_n,$ where $S_n=\\sum_{k=1}^n\\frac{1}{n}-\\log(n+1),$ by linear forms in logarithms and harmonic numbers. In 1995, C. Elsner showed that slow convergence of the sequence $S_n$ can be significantly improved if $S_n$ is replaced by linear combinations of $S_n$ with integer coefficients. In this paper, considering more general linear transformations of the sequence $S_n$ we establish new accelerating convergence formulae for $\\gamma.$ Our estimates sharpen and generalize recent Elsner's, Rivoal's and author's results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-21T08:09:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y60",
      "11Y35",
      "41A25"
    ],
    "keywords": [
      "eulers constant",
      "approximations",
      "general linear transformations",
      "slow convergence",
      "authors results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2771H"
    }
  }
}