{
  "id": "2305.02754",
  "version": "v1",
  "published": "2023-05-04T11:44:14.000Z",
  "updated": "2023-05-04T11:44:14.000Z",
  "title": "A lower bound for the beta function",
  "authors": [
    "Tiehong Zhao",
    "Miaokun Wang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We present a new lower bound for Euler's beta function, $B(x,y)$, which states that the inequality \\begin{equation*} B(x,y)>\\frac{x+y}{xy}\\left(1-\\frac{2xy}{x+y+1}\\right) \\end{equation*} holds on $(0,1]\\times(0,1]$, which improves a lower bound obtained by P. Iv\\'{a}dy [12, Theorem, (3.2)] in the case of $0<x+y<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-04T11:44:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "eulers beta function",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}