{
  "id": "math/0406338",
  "version": "v3",
  "published": "2004-06-17T03:37:44.000Z",
  "updated": "2017-10-15T17:52:17.000Z",
  "title": "On Some Sums of Digamma and Polygamma functions - Version (2017) and Review",
  "authors": [
    "Michael Milgram"
  ],
  "comment": "This (2017) version contains major enhancements and additions to the previous (2004) version",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard reference works or the literature, but which periodically arise in applications, are collected, reviewed, listed and developed to the point that a knowledgeable reader could devise a formal proof. Several errors in the literature are corrected",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-07-07T20:24:52.000Z",
      "title": "On Some Sums of Digamma and Polygamma functions",
      "abstract": "Many formula involving sums of digamma and polygamma functions, few of which appear in standard reference works or the literature, but which commonly arise in applications, are collected and developed. Along the way, a new evaluation for some particular members of the family of hypergeometric functions - 4F3(1) - is presented, and a connection is made with Euler sums. All proofs are sketched.",
      "comment": "minor corrections and additions",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-10-15T17:52:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "33C20",
      "30-02",
      "30B99",
      "33-02",
      "40-02",
      "40C99"
    ],
    "keywords": [
      "polygamma functions",
      "standard reference works",
      "hypergeometric functions",
      "euler sums",
      "commonly arise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6338M"
    }
  }
}