{
  "id": "1802.01473",
  "version": "v1",
  "published": "2018-02-05T15:52:27.000Z",
  "updated": "2018-02-05T15:52:27.000Z",
  "title": "A $q$-analogue of Euler's formula $ζ(2)=π^2/6$",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "It is well known that $\\zeta(2)=\\pi^2/6$ as discovered by Euler. In this paper we establish the following $q$-analogue of this celebrated formula: $$\\sum_{k=0}^\\infty\\frac{q^k(1+q^{2k+1})}{(1-q^{2k+1})^2}=\\prod_{n=1}^\\infty\\frac{(1-q^{2n})^4}{(1-q^{2n-1})^4},$$ where $q$ is any complex number with $|q|<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-05T15:52:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "05A30",
      "11M06",
      "11P84",
      "33D05"
    ],
    "keywords": [
      "eulers formula",
      "complex number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}