Integral Evaluation of Odd Euler Sums, Multiple $t$-Value $t\left(3,2,\dots ,2\right)$ and Multiple Zeta Value $\zeta (3,2,\dots ,2)$

Abstract

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta (3,2,\dots ,2)$ and multiple $t$-value $t\left(3,2,\dots ,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value $t\left(2,\dots ,2,1\right)$.

17 pages