{
  "id": "2205.06247",
  "version": "v1",
  "published": "2022-05-12T17:45:19.000Z",
  "updated": "2022-05-12T17:45:19.000Z",
  "title": "Linear transformations of Srivastava's $H_C$ triple hypergeometric function",
  "authors": [
    "S. Friot",
    "G. Suchet-Bernard"
  ],
  "comment": "16 pages, 2 figures, 1 ancillary file",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We explore the large set of linear transformations of Srivastava's $H_C$ triple hypergeometric function. This function has been recently linked to the massive one-loop conformal scalar 3-point Feynman integral. We focus here on the class of linear transformations of $H_C$ that can be obtained from linear transformations of the Gauss $_2F_1$ hypergeometric function and, as $H_C$ is also a three variable generalization of the Appell $F_1$ double hypergeometric function, from the particular linear transformation of $F_1$ known as Carlson's identity and some of its generalizations. These transformations are applied at the level of the 3-fold Mellin-Barnes representation of $H_C$. This allows us to use the powerful conic hull method of Phys. Rev. Lett. 127 (2021) no.15, 151601 for the evaluation of the transformed Mellin-Barnes integrals, which leads to the desired results. The latter can then be checked numerically against the Feynman parametrization of the conformal 3-point integral. We also show how this approach can be used to derive many known (and less known) results involving Appell double hypergeometric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-12T17:45:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear transformation",
      "triple hypergeometric function",
      "srivastavas",
      "powerful conic hull method",
      "appell double hypergeometric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}