{
  "id": "2105.01880",
  "version": "v1",
  "published": "2021-05-05T05:59:55.000Z",
  "updated": "2021-05-05T05:59:55.000Z",
  "title": "Hankel Determinants of shifted sequences of Bernoulli and Euler numbers",
  "authors": [
    "Karl Dilcher",
    "Lin Jiu"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit, the situation often changes significantly. In this paper we use classical orthogonal polynomials and related methods to prove a general result concerning Hankel determinants for shifted sequences. We then apply this result to obtain new Hankel determinant evaluations for a total of $13$ sequences related to Bernoulli and Euler numbers, one of which concerns Euler polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-05T05:59:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "33D45",
      "11C20"
    ],
    "keywords": [
      "euler numbers",
      "shifted sequences",
      "general result concerning hankel determinants",
      "concerns euler polynomials",
      "hankel determinant evaluations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}