{
  "id": "1901.03368",
  "version": "v1",
  "published": "2019-01-03T03:08:47.000Z",
  "updated": "2019-01-03T03:08:47.000Z",
  "title": "On Positivities of Certain q-Special Functions",
  "authors": [
    "Ruiming Zhang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this work we shall apply the Bochner's theorem to prove certain combinations of Euler's q-exponentials are positive definite functions. Then we apply this positivity to prove curious inequalities for the Jacobi theta function $\\vartheta_{4}$ and q-Gamma function $\\Gamma_{q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-03T03:08:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-special functions",
      "positivity",
      "jacobi theta function",
      "q-gamma function",
      "eulers q-exponentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}