We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space, and to obtain fast converging series representations in each region. We illustrate our approach on the examples of hypergeometric functions that evaluate to iterated Eisenstein integrals as well as the well-known sunrise graph.

中文翻译：

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迭代爱森斯坦积分的算法和工具

我们提出了处理最近出现在多环费曼积分计算中的迭代艾森斯坦积分的算法。这些算法允许人们分析地将这些积分延续到参数空间的所有区域，并在每个区域中获得快速收敛的序列表示。我们用超几何函数的例子来说明我们的方法，这些函数对迭代的爱森斯坦积分以及众所周知的日出图进行评估。