{
  "id": "2407.13936",
  "version": "v1",
  "published": "2024-07-18T23:29:32.000Z",
  "updated": "2024-07-18T23:29:32.000Z",
  "title": "Uniform asymptotic expansions for the zeros of parabolic cylinder functions",
  "authors": [
    "T. M. Dunster",
    "A. Gil",
    "D. Ruiz-Antolin",
    "J. Segura"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-18T23:29:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "33C45",
      "34E20",
      "34C10",
      "33F05"
    ],
    "keywords": [
      "parabolic cylinder function",
      "uniform asymptotic expansions",
      "complex zeros",
      "airy functions",
      "absolute value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}