{
  "id": "2103.13249",
  "version": "v1",
  "published": "2021-03-24T15:08:22.000Z",
  "updated": "2021-03-24T15:08:22.000Z",
  "title": "New Proofs of the Basel Problem using Stochastic Processes",
  "authors": [
    "Uwe Hassler",
    "Mehdi Hosseinkouchack"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The number $\\frac{\\pi ^{2}}{6}$ is involved in the variance of several distributions in statistics. At the same time it holds $\\sum\\nolimits_{k=1}^{\\infty }k^{-2}= \\frac{\\pi ^{2}}{6}$, which solves the famous Basel problem. We first provide a historical perspective on the Basel problem, and second show how to generate further proofs building on stochastic processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-24T15:08:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "01A45",
      "01A50"
    ],
    "keywords": [
      "stochastic processes",
      "famous basel problem",
      "statistics",
      "distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}