{
  "id": "2010.11759",
  "version": "v1",
  "published": "2020-10-22T14:32:28.000Z",
  "updated": "2020-10-22T14:32:28.000Z",
  "title": "Asymptotic evaluation of $\\int_0^\\infty\\left(\\frac{\\sin x}{x}\\right)^n\\;dx$",
  "authors": [
    "Jan-Christoph Schlage-Puchta"
  ],
  "journal": "Commun. Korean Math. Soc. 35 (2020), 1193-1202",
  "doi": "10.4134/CKMS.c200133",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the integral $\\int_0^\\infty\\left(\\frac{\\sin x}{x}\\right)^n\\;dx$ as a function of the positive integer $n$. We show that there exists an asymptotic series in $\\frac{1}{n}$ and compute the first terms of this series together with an explicit error bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-22T14:32:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "33F05"
    ],
    "keywords": [
      "asymptotic evaluation",
      "explicit error bound",
      "asymptotic series",
      "first terms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}