{
  "id": "1705.01190",
  "version": "v1",
  "published": "2017-05-02T22:26:48.000Z",
  "updated": "2017-05-02T22:26:48.000Z",
  "title": "Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions",
  "authors": [
    "T. M. Dunster",
    "A. Gil",
    "J. Segura"
  ],
  "comment": "Submitted to Advances in Computational Mathematics",
  "categories": [
    "math.CA"
  ],
  "abstract": "Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials $L_{n}^{(\\alpha)}(x)$, as well as complementary confluent hypergeometric functions. The expansions are valid for $n$ large and $\\alpha$ small or large, uniformly for unbounded real and complex values of $x$. The new expansions extend the range of computability of $L_n^{(\\alpha)}(x)$ compared to previous expansions, in particular with respect to higher terms and large values of $\\alpha$. Numerical evidence of their accuracy for real and complex values of $x$ is provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-02T22:26:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34E05",
      "33C45",
      "33C15",
      "34E20",
      "33F05"
    ],
    "keywords": [
      "uniform asymptotic expansions",
      "related confluent hypergeometric functions",
      "laguerre polynomials",
      "complementary confluent hypergeometric functions",
      "complex values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}