{
  "id": "1910.06928",
  "version": "v1",
  "published": "2019-10-15T17:04:04.000Z",
  "updated": "2019-10-15T17:04:04.000Z",
  "title": "The binomial transform of p-recursive sequences and the dilogarithm function",
  "authors": [
    "Stephanie L. Harshbarger",
    "Barton L. Willis"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "Using a generalized binomial transform and a novel binomial coefficient identity, we will show that the set of p-recursive sequences is closed under the binomial transform. Using these results, we will derive a new series representation for the dilogarithm function that converges on $\\mathbf{C} \\, \\backslash \\, [1,\\infty)$. Finally, we will show that this series representation results in a scheme for numerical evaluation of the dilogarithm function that is accurate, efficient, and stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T17:04:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E20"
    ],
    "keywords": [
      "dilogarithm function",
      "p-recursive sequences",
      "novel binomial coefficient identity",
      "series representation results",
      "generalized binomial transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}