{
  "id": "1901.01648",
  "version": "v1",
  "published": "2019-01-07T02:40:39.000Z",
  "updated": "2019-01-07T02:40:39.000Z",
  "title": "A digression on Hermite polynomials",
  "authors": [
    "Keith Y. Patarroyo"
  ],
  "comment": "43 pages, 4 figures, survey article",
  "categories": [
    "math.NA"
  ],
  "abstract": "Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite polynomials and show a few of their applications in the connection problem of polynomials, probability theory and the combinatorics of a simple graph. Most of the content presented here is well known, except for a few sections where we add our own work to the subject, nevertheless, the text is meant to be a self-contained personal exposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-07T02:40:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45"
    ],
    "keywords": [
      "hermite polynomials",
      "digression",
      "orthogonal polynomials",
      "self-contained personal exposition",
      "fundamental importance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}