论文标题
交替的Apéry-Type系列和彩色的多个Zeta值八级
Alternating Apéry-Type Series and Colored Multiple Zeta Values of Level Eight
论文作者
论文摘要
近年来Feynman积分的计算中，Apéry-Type（反）二项式系列显着出现。在我们先前的工作中，我们表明，可以使用第四级的有色多个ZETA值（即，在Unity的第四个根基上）使用有色的多个ZETA值（即，多个聚类的特殊值）通过以迭代的积分来表达它们。在此续集中，我们将证明，对于几类交替版本，我们需要将水平提高到八个。我们的主要思想是采用双曲线三角1形式来替换非替代环境中使用的普通三角学。
Apéry-type (inverse) binomial series have appeared prominently in the calculations of Feynman integrals in recent years. In our previous work, we showed that a few large classes of the non-alternating Apéry-type (inverse) central binomial series can be evaluated using colored multiple zeta values of level four (i.e., special values of multiple polylogarithms at fourth roots of unity) by expressing them in terms of iterated integrals. In this sequel, we shall prove that for several classes of the alternating versions we need to raise the level to eight. Our main idea is to adopt hyperbolic trigonometric 1-forms to replace the ordinary trigonometric ones used in the non-alternating setting.
