{
  "id": "2001.03815",
  "version": "v1",
  "published": "2020-01-12T00:45:28.000Z",
  "updated": "2020-01-12T00:45:28.000Z",
  "title": "Addition formulas for the $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with arbitrary parameters and their Kummer- and Euler-type transformations",
  "authors": [
    "Krishna Choudhary"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We obtain addition formulas for $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with general parameters. These are utilized in conjunction with integral representations of these functions to derive Kummer- and Euler-type transformations that express $_{p}F_{p}\\left(x\\right)$ and $_{p+1}F_p\\left(x\\right)$ in the form of sums of $_{p}F_{p}\\left(-x\\right)$ and $_{p+1}F_p\\left(-x\\right)$ functions, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-12T00:45:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "44A20",
      "65B10"
    ],
    "keywords": [
      "generalized hypergeometric functions",
      "addition formulas",
      "euler-type transformations",
      "arbitrary parameters",
      "general parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}