论文标题
Srivastava的$ H_C $三重超几何功能的线性变换
Linear transformations of Srivastava's $H_C$ triple hypergeometric function
论文作者
论文摘要
我们探索了Srivastava的$ H_C $三重超几何功能的大量线性变换。该功能最近与大型的单环标量标量3点Feynman积分链接。我们在这里关注$ h_c $的线性转换类别，可以从高斯的线性变换中获得$ _2F_1 $超测定功能，并且作为$ h_c $也是上appell $ f_1 $双重地质功能的三个可变概括，从$ f_1的特定线性转换为$ f_1 $ for_1 $ nath $ f_1 $ sidentiz $ sidentation and Carlson的识别率和某些常规率。这些转换应用于$ H_C $的3倍Mellin-Barnes表示的级别。这使我们可以使用强大的锥体船体方法。莱特牧师。 127（2021）No.15，151601用于评估转化后的Mellin-Barnes积分，这导致了期望的结果。然后，可以针对共形3点积分的Feynman参数化检查后者。我们还展示了如何使用这种方法来得出许多涉及Appell双重测量功能的已知（鲜为人知的）结果。
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.
