On three general forms of multiple zeta(-star) values

Abstract

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\le 2$ and the evaluation of ${\zeta }^{\star }({\left\{1\right\}}^m,{\left\{2\right\}}^{n+1})$. We also give a new proof of the sum formula of multiple zeta values.