{
  "id": "1808.05105",
  "version": "v1",
  "published": "2018-08-15T14:47:37.000Z",
  "updated": "2018-08-15T14:47:37.000Z",
  "title": "Inequalities for some basic hypergeometric functions",
  "authors": [
    "S. I. Kalmykov",
    "D. B. Karp"
  ],
  "comment": "12 pages; no figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur\\'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-15T14:47:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "26A51"
    ],
    "keywords": [
      "heines basic hypergeometric function",
      "inequalities",
      "logarithmic concavity",
      "higher order regularized basic hypergeometric",
      "order regularized basic hypergeometric function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}