{
  "id": "2303.07664",
  "version": "v2",
  "published": "2023-03-14T07:09:43.000Z",
  "updated": "2024-08-12T11:19:42.000Z",
  "title": "Two closed-form evaluations for the generalized hypergeometric function ${}_4F_3(\\frac1{16})$",
  "authors": [
    "Arjun K. Rathie",
    "Mykola A. Shpot"
  ],
  "comment": "Updated version with new references",
  "categories": [
    "math.CA"
  ],
  "abstract": "The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function $_4F_3$ of the argument $\\frac1{16}$. This is achieved by means of separating a generalized hypergeometric function $_3F_2$ into even and odd components, together with the use of two known results for $_3F_2(\\pm\\frac14)$ available in the literature. As an application, we obtain an interesting infinite-sum representation for the number $\\pi^2$. Certain connections with the work of Ramanujan and other authors are discussed, involving other special functions and binomial sums of different kinds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-08-12T11:19:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "33C05",
      "33C15"
    ],
    "keywords": [
      "generalized hypergeometric function",
      "closed-form evaluations",
      "odd components",
      "binomial sums",
      "interesting infinite-sum representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}