{
  "id": "2204.08275",
  "version": "v1",
  "published": "2022-04-11T16:39:25.000Z",
  "updated": "2022-04-11T16:39:25.000Z",
  "title": "Evaluations of three series of the type $\\sum_{k=0}^\\infty(ak+b)x^k/\\binom{4k}{2k}$",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In this paper, via the beta function we obtain the following three new identities: $$\\sum_{k=0}^\\infty\\frac{k4^k}{\\binom{4k}{2k}}=\\frac{3\\pi+8}{12}, \\ \\ \\ \\ \\sum_{k=0}^\\infty\\frac{(30k-7)(-2)^k}{\\binom{4k}{2k}}=-\\frac{3\\pi+64}{6},$$ and $$\\sum_{k=0}^\\infty\\frac{14k-5}{4^k\\binom{4k}{2k}}=\\frac{16}{81}(\\log2-24).$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-11T16:39:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "05A19",
      "11A07",
      "33B15"
    ],
    "keywords": [
      "evaluations",
      "beta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}