{
  "id": "math/0601078",
  "version": "v1",
  "published": "2006-01-04T18:54:49.000Z",
  "updated": "2006-01-04T18:54:49.000Z",
  "title": "Asymptotic analysis of the Hermite polynomials from their differential-difference equation",
  "authors": [
    "Diego Dominici"
  ],
  "comment": "21 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We analyze the Hermite polynomials $H_{n}(x)$ and their zeros asymptotically, as $n\\to\\infty.$ We obtain asymptotic approximations from the differential-difference equation which they satisfy, using the ray method. We give numerical examples showing the accuracy of our formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-04T18:54:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "34E05",
      "34E20"
    ],
    "keywords": [
      "hermite polynomials",
      "differential-difference equation",
      "asymptotic analysis",
      "asymptotic approximations",
      "ray method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1078D"
    }
  }
}