论文标题
Kaneko之间的显式关系 - Yamamoto类型多个Zeta值和相关变体
Explicit Relations between Kaneko--Yamamoto Type Multiple Zeta Values and Related Variants
论文作者
论文摘要
在本文中，我们首先建立了几个不可或缺的身份。这些积分的形式为\ [\ int_0^1 x^{an+b} f（x）\，dx \ quad（a \ in \ in \ {1,2 \}，\ b \ in \ in \ in \ in \ { - 1，-2，-2 \}）$ f（x）$是$ f（x）$是单个多个poligh poligh poligh unigh unighm $ $ $ $或kaneko--tsumura a功能（这是二级的单个多元多组载体函数）。我们发现这些积分可以用多个Zeta（Star）值及其相关变体表示（多个$ t $值，多个$ t $ - 值，多个$ s $ values等）和多个谐波（star）和其相关变体（多个$ t $ harmonic sums，多个$ s $ -sharmonic sums等）。使用这些积分身份，我们证明了kaneko的许多明确评估 - 育采对多个Zeta值及其相关变体。此外，我们得出了一些涉及多个Zeta（Star）值及其相关变体的关系。
In this paper we first establish several integral identities. These integrals are of the form \[\int_0^1 x^{an+b} f(x)\,dx\quad (a\in\{1,2\},\ b\in\{-1,-2\})\] where $f(x)$ is a single-variable multiple polylogarithm function or $r$-variable multiple polylogarithm function or Kaneko--Tsumura A-function (this is a single-variable multiple polylogarithm function of level two). We find that these integrals can be expressed in terms of multiple zeta (star) values and their related variants (multiple $t$-values, multiple $T$-values, multiple $S$-values etc.), and multiple harmonic (star) sums and their related variants (multiple $T$-harmonic sums, multiple $S$-harmonic sums etc.). Using these integral identities, we prove many explicit evaluations of Kaneko--Yamamoto multiple zeta values and their related variants. Further, we derive some relations involving multiple zeta (star) values and their related variants.
