Explicit formulas of alternating multiple zeta star values ${\zeta }^{\star }(\overline{1},\{1{\}}_{m-1},\overline{1})$ and ${\zeta }^{\star }(2,\{1{\}}_{m-1},\overline{1})$

In a recent paper ^[4], Xu studied some alternating multiple zeta values. In particular, he gave two recurrence formulas of alternating multiple zeta values ${\zeta }^{\star }(\overline{1},\{1{\}}_{m-1},\overline{1})$ and ${\zeta }^{\star }(2,\{1{\}}_{m-1},\overline{1})$. In this paper, we will give the closed forms representations of ${\zeta }^{\star }(\overline{1},\{1{\}}_{m-1},\overline{1})$ and ${\zeta }^{\star }(2,\{1{\}}_{m-1},\overline{1})$ in terms of single zeta values and polylogarithms.