{
  "id": "math/0306233",
  "version": "v1",
  "published": "2003-06-16T01:03:01.000Z",
  "updated": "2003-06-16T01:03:01.000Z",
  "title": "The best bounds of harmonic sequence",
  "authors": [
    "Chao-Ping Chen",
    "Feng Qi"
  ],
  "comment": "5 pages",
  "journal": "Chao-Ping Chen and Feng Qi, The best bounds of the $n$-th harmonic number, Global Journal of Applied Mathematics and Mathematical Sciences 1 (2008), no. 1, 41--49",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "For any natural number $n\\in\\mathbb{N}$, $ \\frac{1}{2n+\\frac1{1-\\gamma}-2}\\le \\sum_{i=1}^n\\frac1i-\\ln n-\\gamma<\\frac{1}{2n+\\frac13}, $ where $\\gamma=0.57721566490153286...m$ denotes Euler's constant. The constants $\\frac{1}{1-\\gamma}-2$ and $\\frac13$ are the best possible. As by-products, two double inequalities of the digamma and trigamma functions are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-16T01:03:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "33B15"
    ],
    "keywords": [
      "harmonic sequence",
      "best bounds",
      "denotes eulers constant",
      "natural number",
      "trigamma functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6233C"
    }
  }
}