论文标题
一种用于嵌套总和和高几何扩展的新型算法
A Novel Algorithm for Nested Summation and Hypergeometric Expansions
论文作者
论文摘要
我们考虑Z-SUM的产品的一类总和，其论点因符号整数而不同。例如，在围绕符号参数的整数索引的高点函数的扩展中，出现了这样的总和。我们提出了一种伸缩算法，以有效地将这些总和转换为通用的聚类，z-sums和环形谐波和该参数的通用值。通过通过十个循环计算双重PentalAdder积分来说明该算法，以及通过$ O（ε^6）$中的一个大规模的自我能量图中的一家在维度正则化中。我们还概述了该算法的一般伸缩策略，我们预计可以将其应用于其他类别的总和。
We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that depend on a symbolic parameter. We present a telescopic algorithm for efficiently converting these sums into generalized polylogarithms, Z-sums, and cyclotomic harmonic sums for generic values of this parameter. This algorithm is illustrated by computing the double pentaladder integrals through ten loops, and a family of massive self-energy diagrams through $O(ε^6)$ in dimensional regularization. We also outline the general telescopic strategy of this algorithm, which we anticipate can be applied to other classes of sums.
