{
"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"
}
}
}