{
  "id": "1510.01285",
  "version": "v1",
  "published": "2015-10-05T19:06:57.000Z",
  "updated": "2015-10-05T19:06:57.000Z",
  "title": "On the zeros of Confluent Hypergeometric Functions",
  "authors": [
    "Wei-Chuan Lin",
    "Xu-Dan Luo"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.CV",
    "math.MP"
  ],
  "abstract": "In this paper, we study the zero sets of the confluent hypergeometric function $_{1}F_{1}(\\alpha;\\gamma;z):=\\sum_{n=0}^{\\infty}\\frac{(\\alpha)_{n}}{n!(\\gamma)_{n}}z^{n}$, where $\\alpha, \\gamma, \\gamma-\\alpha\\not\\in \\mathbb{Z}_{\\leq 0}$, and show that if $\\{z_n\\}_{n=1}^{\\infty}$ is the zero set of $_{1}F_{1}(\\alpha;\\gamma;z)$ with multiple zeros repeated and modulus in increasing order, then there exists a constant $M>0$ such that $|z_n|\\geq M n$ for all $n\\geq 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-05T19:06:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "30D30",
      "30D35"
    ],
    "keywords": [
      "confluent hypergeometric function",
      "zero set",
      "multiple zeros",
      "increasing order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}