{
  "id": "2405.16814",
  "version": "v1",
  "published": "2024-05-27T04:16:39.000Z",
  "updated": "2024-05-27T04:16:39.000Z",
  "title": "Series Associated with Harmonic Numbers, Fibonacci Numbers and Central Binomial Coefficients $\\binom{2n}{n}$",
  "authors": [
    "Akerele Olofin Segun"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We find various series that involves the central binomial coefficients $\\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward transformation to obtain new evaluations linked to Fibonacci numbers and the golden ratio. Before the end of this paper, we also gave a new series representation for $\\zeta(2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-27T04:16:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A05",
      "11B39",
      "11B65",
      "05A10"
    ],
    "keywords": [
      "central binomial coefficients",
      "fibonacci numbers",
      "harmonic numbers",
      "traditional hypergeometric function",
      "golden ratio"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}