论文标题
多个Zeta值与相关变体之间的明确关系
Explicit Relations between Multiple Zeta Values and Related Variants
论文作者
论文摘要
在本文中，我们通过使用对数函数的迭代积分计算的方法，介绍了多种聚类（Abbr。mpls）和多个谐波星和多个谐波星总和（Abbr。MHSS）的一些新身份。然后，通过应用这些获得的这些公式，我们在Kaneko-Yamamoto型多重Zeta值（Abbr。K-Y MZV），多个Zeta值（Abbr。MZV）和MPLS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（ABBR。MZSVS）之间的一些明确关系。此外，我们定义了mzsvs $ζ^\ star_b（{\ bf k}）$（称为多个zeta $ b $ star值，abbr。mzbsvs）的apéry-type变体，涉及MHSSS和中央二元组合，并建立MIMZVS，MHSSS和中央二元组中的MIMZV，MZVSSS和中央二元组中的MMZVEV，迭代积分。最后，提出了一些有趣的后果和说明性的例子。
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 $ζ^\star_B({\bf k})$ (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.
