Some identities for multiple zeta values

被引：24

作者：

Shen, Zhongyan ^{[1
,2
]}

Cai, Tianxin ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Zhejiang Int Study Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Multiple zeta values; Harmonic shuffle relation; Bernoulli numbers;

D O I：

10.1016/j.jnt.2011.06.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we obtain the following identities, Sigma(a+b+c=n) zeta(2a, 2b, 2c) = 5/8 zeta(2n) - 1/4 zeta(2)zeta(2n - 2), for n > 2, Sigma(a+b+c+d=n) zeta(2a, 2b, 2c, 2d) = 35/64 zeta(2n) - 5/16 zeta(2)zeta(2n - 2), for n > 3. Meanwhile, some weighted version of sum formulas are also obtained. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：314 / 323

页数：10

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