Some Symmetry and Duality Theorems on Multiple Zeta(-star) Values

Abstract: In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. Leveraging Zagier's formula for computing $\zeta^\star({2}^p,3,{2}^q)$, we employ our theorems to establish a formula for computing $\zeta^\star({2}^p,1,{2}^q)$ for any positive integers $p$ and $q$, along with other formulas of interest.