EXPLICIT RELATIONS BETWEEN KANEKO-YAMAMOTO TYPE MULTIPLE ZETA VALUES AND RELATED VARIANTS

IF 0.6 4区 数学 Q3 MATHEMATICS
Ce Xu, Jianqiang Zhao
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引用次数: 5

Abstract

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.
KANEKO-YAMAMOTO型多重ζ值及其变异的显式关系
本文首先建立了几个积分恒等式。这些积分的形式为\[\int_0^1 x^{an+b}f(x)\,dx\quad(a\in\{1,2\},\b\in\(-1,-2\}))\],其中$f(x。我们发现,这些积分可以用多个ζ(星)值及其相关变体(多个$t$-值、多个$t$-值和多个$S$-值等)和多个调和(星)和及其相关变体。使用这些积分恒等式,我们证明了Kaneko-Yamamoto多重ζ值及其相关变体的许多显式评价。此外,我们还推导了一些涉及多个ζ(恒星)值及其相关变体的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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