论文标题
appell $ f_4 $系列的新分析延续来自高斯的二次变换$ _ {2} f_1 $函数
New analytic continuations for the Appell $F_4$ series from quadratic transformations of the Gauss $_{2}F_1$ function
论文作者
论文摘要
我们为Appell $ f_4（a，b; c，d; x，y）介绍了新的分析延续公式，其中$ d = a-b+1 $，这允许高斯$ {} _ 2f_1 $超测量函数的二次变换，可以在衍生的中间步骤中使用。这种公式与量子场理论的循环计算相关，例如，它们可以使用它们来获取两循环大量日落Feynman图的新序列表示。本文介绍的分析延续程序也足够一般，以便在其他地方找到用途。
We present new analytic continuation formulas for the Appell $F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows quadratic transformations of the Gauss ${}_2F_1$ hypergeometric function to be used in the intermediate steps of the derivation. Such formulas are of relevance to loop calculations of quantum field theory where they can been used, for instance, to obtain new series representations of the two-loop massive sunset Feynman diagram. The analytic continuation procedure introduced in this paper is also sufficiently general so as to find uses elsewhere.
