{
  "id": "math/0402354",
  "version": "v5",
  "published": "2004-02-22T22:36:20.000Z",
  "updated": "2005-05-25T01:18:15.000Z",
  "title": "Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series",
  "authors": [
    "Mark B. Villarino"
  ],
  "comment": "7 pages. Numerical copy error corrected as well as the computations based on it. Minor expository improvements",
  "categories": [
    "math.CA"
  ],
  "abstract": "A simple integration by parts and telescopic cancellation leads to a rigorous derivation of the first 2 terms for the error in Ramanujan's asymptotic series for the nth partial sum of the harmonic series. Then Kummer's transformation gives three more terms and a rigorous error estimate. Finally best-possible estimates of Lodge's approximations.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-05-25T01:18:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A25"
    ],
    "keywords": [
      "nth partial sum",
      "harmonic series",
      "ramanujans approximation",
      "ramanujans asymptotic series",
      "simple integration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2354V"
    }
  }
}