{
  "id": "1508.03948",
  "version": "v1",
  "published": "2015-08-17T08:32:33.000Z",
  "updated": "2015-08-17T08:32:33.000Z",
  "title": "An asymptotic expansion for the Stieltjes constants",
  "authors": [
    "R. B. Paris"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "The Stieltjes constants $\\gamma_n$ appear in the coefficients in the Laurent expansion of the Riemann zeta function $\\zeta(s)$ about the simple pole $s=1$. We present an asymptotic expansion for $\\gamma_n$ as $n\\rightarrow \\infty$ based on the approach described by Knessel and Coffey [Math. Comput. {\\bf 80} (2011) 379--386]. A truncated form of this expansion with explicit coefficients is also given. Numerical results are presented that illustrate the accuracy achievable with our expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-17T08:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E20",
      "34E05",
      "41A60",
      "11M06"
    ],
    "keywords": [
      "stieltjes constants",
      "asymptotic expansion",
      "riemann zeta function",
      "explicit coefficients",
      "simple pole"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803948P"
    }
  }
}