Identities for the Multiple Zeta (Star) Values

Abstract

In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By applying the formulas obtained, we prove that the multiple zeta star values whose indices are the sequences $$(\bar{1},\{1\}_m,\bar{1})$$ and $$(2,\{1\}_m,\bar{1})$$ can be expressed polynomially in terms of zeta values, polylogarithms and $$\ln (2)$$ . We also evaluate several restricted sums involving multiple zeta values.