{
  "id": "2105.00686",
  "version": "v1",
  "published": "2021-05-03T08:45:56.000Z",
  "updated": "2021-05-03T08:45:56.000Z",
  "title": "The asymptotic expansion of the Bernoulli polynomials of the second kind",
  "authors": [
    "R B Paris"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the Bernoulli polynomials of the second kind, which can be related to the generalised Bernoulli polynomials $B_n^{(n)}(z)$. The asymptotic expansions of the scaled polynomials $B_n^{(n)}(nz)$ are obtained as $n\\to\\infty$ when (i) $z$ is real and (ii) $z$ is complex bounded away from $[0,1]$. These results complement recent work of \\v{S}tampach [{\\it J. Approx. Theory}, {\\bf 262} (2021) 105517]. Numerical results are presented to illustrate the accuracy of the different expansions obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-03T08:45:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "34E05",
      "41A30",
      "41A60"
    ],
    "keywords": [
      "second kind",
      "asymptotic expansion",
      "generalised bernoulli polynomials",
      "complex bounded away",
      "results complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}