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Zbl 1229.11119
Shen, Zhongyan; Cai, Tianxin
Some identities for multiple zeta values.
(English)
[J] J. Number Theory 132, No. 2, 314-323 (2012). ISSN 0022-314X; ISSN 1096-1658/e

Summary: In this note, we obtain the following identities, $$\sum_{a+b+c=n} \zeta(2a,2b,2c)=\frac 58 \zeta(2n)-\frac 14 \zeta(2)\zeta(2n-2),\quad\text{for}\, n>2,$$ $$\sum_{a+b+c+d=n} \zeta(2a,2b,2c,2d)=\frac{35}{64} \zeta(2n)-\frac 5{16} \zeta(2)\zeta(2n-2),\quad\text{for}\, n>3,$$ Meanwhile, some weighted version of sum formulas are also obtained.
MSC 2000:
*11M32
11B68 Bernoulli numbers, etc.

Keywords: multiple zeta values; harmonic shuffle relation; Bernoulli numbers

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