{
  "id": "1906.12023",
  "version": "v1",
  "published": "2019-06-28T02:59:40.000Z",
  "updated": "2019-06-28T02:59:40.000Z",
  "title": "Evaluation of Abramowitz functions in the right half of the complex plane",
  "authors": [
    "Zydrunas Gimbutas",
    "Shidong Jiang",
    "Li-Shi Luo"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A numerical scheme is developed for the evaluation of Abramowitz functions $J_n$ in the right half of the complex plane. For $n=-1,\\, \\ldots,\\, 2$, the scheme utilizes series expansions for $|z|<1$ and asymptotic expansions for $|z|>R$ with $R$ determined by the required precision, and modified Laurent series expansions which are precomputed via a least squares procedure to approximate $J_n$ accurately and efficiently on each sub-region in the intermediate region $1\\le |z| \\le R$. For $n>2$, $J_n$ is evaluated via a recurrence relation. The scheme achieves nearly machine precision for $n=-1, \\ldots, 2$, with the cost about four times of evaluating a complex exponential per function evaluation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-28T02:59:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E20",
      "33F05",
      "65D15",
      "65E05",
      "65F99"
    ],
    "keywords": [
      "complex plane",
      "right half",
      "abramowitz functions",
      "scheme utilizes series expansions",
      "modified laurent series expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}