{
  "id": "2403.03912",
  "version": "v2",
  "published": "2024-03-06T18:15:49.000Z",
  "updated": "2024-03-07T13:54:41.000Z",
  "title": "Digamma function and general Fischer series in the theory of Kempner sums",
  "authors": [
    "Jean-François Burnol"
  ],
  "comment": "9 pages. v2 extended the comments after the main theorem and slightly changed the introduction",
  "categories": [
    "math.NT"
  ],
  "abstract": "The infinite sum of reciprocals of the integers which are missing specified digits (from a given base) is computed with the help of the digamma function as a series involving the zeta values at integers and certain quantities which are rational in the base. This generalizes the work of Fischer (1993) who had handled the original \"no $9$ in base $10$\" case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-03-07T13:54:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y60",
      "11M06",
      "11A63",
      "44A60",
      "30C10"
    ],
    "keywords": [
      "general fischer series",
      "digamma function",
      "kempner sums",
      "infinite sum",
      "zeta values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}