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Explicit relations between multiple zeta values and related variants
Advances in Applied Mathematics ( IF 1.1 ) Pub Date : 2021-06-14 , DOI: 10.1016/j.aam.2021.102245
Ce Xu

In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral computations of logarithm functions. Then, by applying these formulas obtained, we establish some explicit relations between Kaneko-Yamamoto type multiple zeta values (abbr. K-Y MZVs), multiple zeta values (abbr. MZVs) and MPLs. Further, we find some explicit relations between MZVs and multiple zeta star values (abbr. MZSVs). Furthermore, we define an Apéry-type variant of MZSVs ζB(k) (called multiple zeta B-star values, abbr. MZBSVs) which involve MHSSs and central binomial coefficients, and establish some explicit connections among MZVs, alternating MZVs and MZBSVs by using the method of iterated integrals. Finally, some interesting consequences and illustrative examples are presented.



中文翻译:

多个 zeta 值和相关变体之间的显式关系

在本文中,我们通过使用对数函数的迭代积分计算方法,提出了多重多对数(缩写 MPL)和多重谐波星和(缩写 MHSS)的一些新恒等式。然后,通过应用获得的这些公式,我们在 Kaneko-Yamamoto 型多 zeta 值(缩写为 KY MZVs)、多 zeta 值(缩写为 MZVs)和 MPL 之间建立了一些明确的关系。此外,我们发现 MZV 与多个 zeta 星值(简称 MZSV)之间存在一些明确的关系。此外,我们定义了 MZSV 的 Apéry 型变体ζ()(称为多zeta B- star值,简称MZBSVs),它涉及MHSSs和中心二项式系数,并通过使用迭代积分的方法在MZVs、交替MZVs和MZBSVs之间建立了一些显式联系。最后,介绍了一些有趣的结果和说明性示例。

更新日期:2021-06-14
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