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Some identities for multiple zeta values. (English) Zbl 1229.11119
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:
 11M32 Multiple Dirichlet series, etc. 11B68 Bernoulli and Euler numbers and polynomials
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##### References:
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