{
  "id": "1412.4115",
  "version": "v1",
  "published": "2014-12-12T20:57:26.000Z",
  "updated": "2014-12-12T20:57:26.000Z",
  "title": "On approximation measures of $q$-exponential function",
  "authors": [
    "Leena Leinonen",
    "Marko Leinonen",
    "Tapani Matala-aho"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We shall present effective approximations measures for certain infinite products related to $q$-exponential function. There are two main targets. First we shall prove an explicit irrationality measure result for the values of $q$-exponential function at rational points. Then, if we restrict the approximations to rational numbers of the shape $d^s/N$, we may replace Bundschuh's irrationality exponent $7/3$ by $2+\\frac{1}{3+2\\sqrt 3}=2.1547...$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-12T20:57:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J82"
    ],
    "keywords": [
      "exponential function",
      "approximation measures",
      "replace bundschuhs irrationality exponent",
      "explicit irrationality measure result",
      "effective approximations measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4115L"
    }
  }
}