{
  "id": "1805.01999",
  "version": "v1",
  "published": "2018-05-05T04:59:32.000Z",
  "updated": "2018-05-05T04:59:32.000Z",
  "title": "Inequalities for the $q$-gamma and related functions",
  "authors": [
    "Mohamed El Bachraoui",
    "József Sándor"
  ],
  "comment": "Submitted 4 May 2018, pages 16",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider convexity and monotonicity properties for some functions related to the $q$-gamma function. As applications, we give a variety of inequalities for the $q$-gamma function, the $q$-digamma function $\\psi_q(x)$, and the $q$-series. Among other consequences, we improve a result of Azler~and~Grinshpan about the zeros of the function $\\psi_q(x)$. We use $q$-analogues for the Gauss multiplication formula to put in closed form members of some of our inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-05T04:59:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "26D15",
      "33E05"
    ],
    "keywords": [
      "related functions",
      "inequalities",
      "gauss multiplication formula",
      "digamma function",
      "monotonicity properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}