{
  "id": "1903.09070",
  "version": "v1",
  "published": "2019-03-21T15:47:44.000Z",
  "updated": "2019-03-21T15:47:44.000Z",
  "title": "On the necessary condition for entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre-Pólya class",
  "authors": [
    "Thu Hien Nguyen",
    "Anna Vishnyakova"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "For an entire function $f(z) = \\sum_{k=0}^\\infty a_k z^k, a_k>0,$ we show that $f$ does not belong to the Laguerre-P\\'olya class if the quotients $\\frac{a_{n-1}^2}{a_{n-2}a_n}$ are increasing in $n$, and $c:= \\lim\\limits_{n\\to \\infty} \\frac{a_{n-1}^2}{a_{n-2}a_n}$ is smaller than an absolute constant $q_\\infty$ $(q_\\infty\\approx 3{.}2336) .$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-21T15:47:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C15",
      "30D15",
      "30D35",
      "26C10"
    ],
    "keywords": [
      "increasing second quotients",
      "entire function",
      "taylor coefficients",
      "laguerre-pólya class",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}