{
  "id": "2008.02488",
  "version": "v1",
  "published": "2020-08-06T07:27:50.000Z",
  "updated": "2020-08-06T07:27:50.000Z",
  "title": "Tornheim-like series, harmonic numbers and zeta values",
  "authors": [
    "Ilham A. Aliev",
    "Ayhan Dil"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Explicit evaluations of the Tornheim-like double series in the form \\[ \\sum_{n,m=1}^\\infty \\frac{H_{n+m+s}}{nm\\left( n+m+s \\right)},\\ s\\in \\mathbb{N\\cup } \\left\\{ 0 \\right\\} \\] and their extensions are given. Furthermore, series of the type \\[ \\sum_{m=1}^\\infty \\frac{2H_{2m+1}-H_{m}}{2m\\left( 2m+1 \\right)} \\] and some other Tornheim-like multiple series are evaluated in terms of the zeta values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-06T07:27:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A25",
      "40B05",
      "11M06"
    ],
    "keywords": [
      "zeta values",
      "harmonic numbers",
      "tornheim-like series",
      "explicit evaluations",
      "tornheim-like multiple series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}