{
  "id": "2005.06384",
  "version": "v1",
  "published": "2020-05-13T15:50:21.000Z",
  "updated": "2020-05-13T15:50:21.000Z",
  "title": "Exact lower and upper bounds on the incomplete gamma function",
  "authors": [
    "Iosif Pinelis"
  ],
  "comment": "To appear in Mathematical Inequalities & Applications",
  "categories": [
    "math.CA"
  ],
  "abstract": "Lower and upper bounds $B_a(x)$ on the incomplete gamma function $\\Gamma(a,x)$ are given for all real $a$ and all real $x>0$. These bounds $B_a(x)$ are exact in the sense that $B_a(x)\\underset{x\\downarrow0}\\sim\\Gamma(a,x)$ and $B_a(x)\\underset{x\\to\\infty}\\sim\\Gamma(a,x)$. Moreover, the relative errors of these bounds are rather small for other values of $x$, away from $0$ and $\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T15:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B20",
      "26D07",
      "26D15"
    ],
    "keywords": [
      "incomplete gamma function",
      "upper bounds",
      "exact lower",
      "relative errors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}