四维时空的双圈日出积分及Clausen函数和Glausen函数对椭圆情形的推广
The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
摘要：
我们提出的结果的有限部分的两个循环日出积分不等质量的四个时空维的${\mathcal O}(\varepsilon^0)$ -部分和${\mathcal O}(\varepsilon^1)$ -部分的日出积分在两个时空维。后两个积分给出的克劳森和Glausen函数的椭圆推广。有趣的方面的结果${\mathcal O}(\varepsilon^1)$ -一部分的日出积分围绕两个时空维度的发生深度两个椭圆形物体和权重的个别条款。
英文摘要：
We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the ${\mathcal O}(\varepsilon^0)$-part and the ${\mathcal O}(\varepsilon^1)$-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the ${\mathcal O}(\varepsilon^1)$-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.
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