维数递归关系：计算$ε$高阶展开式的一种简便方法
Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in $ε$
摘要：
应用作者之一（R.L.）给出了这种方法是基于使用的维数递归关系和分析性质的费曼积分的功能的维数正则化，$d$的参数。利用该方法得到了对三圈无质量夸克和胶子形状因子有贡献的最复杂主积分的$ε$展开式中两个缺失常数的解析表达式，从而给出了完全解析形式的形状因子.为了说明它的力量，我们提出，在超越性重量7，下一个顺序的$ε$ -扩展相应的最复杂的主积分之一。作为进一步的应用，我们提出了三个以前未知的三圈非平面无质量传播子图的$ε$中的扩展项。在我们的结果中，只存在整数点处的多个$ζ$值。
英文摘要：
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of dimensional regularization, $d$. The method was used to obtain analytical expressions for two missing constants in the $ε$-expansion of the most complicated master integrals contributing to the three-loop massless quark and gluon form factors and thereby present the form factors in a completely analytic form. To illustrate its power we present, at transcendentality weight seven, the next order of the $ε$-expansion of one of the corresponding most complicated master integrals. As a further application, we present three previously unknown terms of the expansion in $ε$ of the three-loop non-planar massless propagator diagram. Only multiple $ζ$ values at integer points are present in our result.
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