{
  "id": "2108.12543",
  "version": "v1",
  "published": "2021-08-28T01:22:41.000Z",
  "updated": "2021-08-28T01:22:41.000Z",
  "title": "Integral representations for local dilogarithm and trilogarithm functions",
  "authors": [
    "Masato Kobayashi"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Catalan constants, and Legendre chi functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-28T01:22:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E20",
      "11G55",
      "11M06",
      "11M41"
    ],
    "keywords": [
      "integral representations",
      "trilogarithm functions",
      "local dilogarithm",
      "unit interval",
      "legendre chi functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}