{
  "id": "1504.07696",
  "version": "v1",
  "published": "2015-04-29T01:45:12.000Z",
  "updated": "2015-04-29T01:45:12.000Z",
  "title": "On a family of polynomials related to $ζ(2,1)=ζ(3)$",
  "authors": [
    "Wadim Zudilin"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.CA",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We give a new proof of the identity $\\zeta(\\{2,1\\}^l)=\\zeta(\\{3\\}^l)$ of the multiple zeta values, where $l=1,2,\\dots$, using generating functions of the underlying generalized polylogarithms. In the course of study we arrive at (hypergeometric) polynomials satisfying 3-term recurrence relations, whose properties we examine and compare with analogous ones of polynomials originated from an (ex-)conjectural identity of Borwein, Bradley and Broadhurst.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-29T01:45:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M41",
      "11G55",
      "33C20"
    ],
    "keywords": [
      "polynomials",
      "multiple zeta values",
      "recurrence relations",
      "conjectural identity",
      "generating functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407696Z"
    }
  }
}