{ "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" } } }