{
  "id": "1808.06522",
  "version": "v1",
  "published": "2018-08-17T10:43:31.000Z",
  "updated": "2018-08-17T10:43:31.000Z",
  "title": "Some hypergeometric summation theorems and reduction formulas via Laplace transform method",
  "authors": [
    "M. I. Qureshi",
    "Showkat Ahmad Dar"
  ],
  "comment": "21 pages, 0 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions ${}_3F_2 (\\pm1)$, ${}_4F_3 (\\pm1)$, ${}_5F_4(\\pm1)$, ${}_6F_5(\\pm1)$, ${}_7F_6(\\pm1)$ and ${}_8F_7(\\pm1)$ with suitable convergence conditions, by using some algebraic properties of Pochhammer symbols. In addition, reduction formulas for ${}_4F_3(1)$, ${}_7F_6(-1)$ and some new summation theorems (not recorded earlier in the literature of hypergeometric functions) for ${}_3F_2(-1)$, ${}_6F_5(\\pm1)$, ${}_7F_6(\\pm1)$ and ${}_8F_7(\\pm1)$ are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-17T10:43:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "33C20",
      "44A10",
      "33B15"
    ],
    "keywords": [
      "hypergeometric summation theorems",
      "laplace transform method",
      "reduction formulas",
      "hypergeometric functions",
      "hyperbolic integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}