{
  "id": "1211.5033",
  "version": "v1",
  "published": "2012-11-20T00:22:25.000Z",
  "updated": "2012-11-20T00:22:25.000Z",
  "title": "A closed-form expression for zeta(2n+1) reveals a self-recursive function",
  "authors": [
    "Michael A. Idowu"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Euler discovered a formula for expressing the value of the Riemann zeta function for all even positive integer arguments. A closed-form expression for the Riemann zeta function for all odd integer arguments, based on the values of the Dirichlet beta function, euler numbers and pi, reveals a new evidence about the self-recursive nature of Riemann zeta function at odd integers. We demonstrate for the first time that the Riemann zeta function at odd integers always produces a recurrence relation that is self-recursive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-20T00:22:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "closed-form expression",
      "self-recursive function",
      "dirichlet beta function",
      "odd integer arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5033I"
    }
  }
}