标题： Srivastava的三重超几何函数$H_C$的线性变换 显示英文标题

标题： Linear transformations of Srivastava's $H_C$ triple hypergeometric function

摘要： 我们研究了Srivastava的三重超几何函数$H_C$的一大类线性变换。 最近已将此函数与质量为一的圈速费曼标量三点积分联系起来。 我们在此集中于一类可以从Gauss超几何函数$_2F_1$的线性变换获得的$H_C$变换，以及由于$H_C$是Appell双变量超几何函数$F_1$的三变量推广，可以从称为Carlson恒等式及其某些推广的$F_1$特定线性变换得到的变换。 这些变换应用于$H_C$的三重Mellin-Barnes表示。 这使得我们可以使用Phys. Rev. Lett. 127 (2021) no.15, 151601中的强力圆锥包络法来评估变换后的Mellin-Barnes积分，从而得到所需的结果。 后者可以与共形三点积分的Feynman参数化进行数值验证。 我们还展示了如何利用这种方法推导出许多已知（和不太为人所知）涉及Appell双变量超几何函数的结果。 显示英文摘要

摘要： 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.