{
  "id": "1002.3856",
  "version": "v1",
  "published": "2010-02-20T07:56:38.000Z",
  "updated": "2010-02-20T07:56:38.000Z",
  "title": "Sharp bounds for harmonic numbers",
  "authors": [
    "Feng Qi",
    "Bai-Ni Guo"
  ],
  "comment": "7 pages",
  "journal": "Bai-Ni Guo and Feng Qi, Sharp bounds for harmonic numbers, Applied Mathematics and Computation 218 (2011), no. 3, 991--995",
  "doi": "10.1016/j.amc.2011.01.089",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\\in\\mathbb{N}$, the double inequality -\\frac{1}{12n^2+{2(7-12\\gamma)}/{(2\\gamma-1)}}\\le H(n)-\\ln n-\\frac1{2n}-\\gamma<-\\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\\frac{2(7-12\\gamma)}{2\\gamma-1}$ and $\\frac65$ are the best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-20T07:56:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "33B15"
    ],
    "keywords": [
      "sharp bounds",
      "bounding harmonic numbers",
      "first survey",
      "euler-mascheroni constant",
      "sharp double inequality"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3856Q"
    }
  }
}