Applications of stuffle product of multiple zeta values

被引：3

作者：

Chen, Kwang-Wu ^{[1
]}

机构：

[1] Univ Taipei, Dept Math, Taipei 10048, Taiwan

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 153卷

关键词：

Multiple zeta value; Stuffle product; Delannoy number; DECOMPOSITION;

D O I：

10.1016/j.jnt.2015.01.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain some formulas for the stuffle product and apply them to derive a decomposition formula for multiple zeta values. Moreover, we give an application to combinatorics and get the following identity: D(n +1, t + 1) + D(n, t) = 2 Sigma D-n(l=0)(t,n - l) + 2 Sigma D-t(l=0)(n, t - l) where D(n, t) is the Delannoy number. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：107 / 116

页数：10

共 10 条

[1] Borwein J.M., 1998, ELECTRON J COMB, V5, P12
[2] Special values of multiple polylogarithms
Borwein, JM
Bradley, DM
Broadhurst, DJ
Lisonek, P
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (03) : 907 - 941
[3] Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
Broadhurst, DJ
Kreimer, D
[J]. PHYSICS LETTERS B, 1997, 393 (3-4) : 403 - 412
[4] Comtet L., 1974, ADV COMBINATORICS
[5] Generalizations of Euler decomposition and their applications
Eie, Minking
Wei, Chuan-Sheng
[J]. JOURNAL OF NUMBER THEORY, 2013, 133 (08) : 2475 - 2495
[6] Guo L., 2012, INTRO ROTA BAXTER AL
[7] The algebra of multiple harmonic series
Hoffman, ME
[J]. JOURNAL OF ALGEBRA, 1997, 194 (02) : 477 - 495
[8] Applications of shuffle product to restricted decomposition formulas for multiple zeta values
Lei, Peng
Guo, Li
Ma, Biao
[J]. JOURNAL OF NUMBER THEORY, 2014, 144 : 219 - 233
[9] On some explicit evaluations of multiple zeta-star values
Muneta, Shuichi
[J]. JOURNAL OF NUMBER THEORY, 2008, 128 (09) : 2538 - 2548
[10] Evaluation of the multiple zeta values ζ(2,...,2,3,2,...,2)
Zagier, D.
[J]. ANNALS OF MATHEMATICS, 2012, 175 (02) : 977 - 1000

← 1 →