On the evaluations of multiple $S$ and $T$ values of the form $S(\stackrel{{}_{(-)}}{2},1,\dots ,1,\stackrel{{}_{(-)}}{1})$ and $T(\stackrel{{}_{(-)}}{2},1,\dots ,1,\stackrel{{}_{(-)}}{1})$

Steven Charlton

Xu, Yan and Zhao showed that in even weight, the multiple $T$ value $T(2,1,\dots ,1,\overline{1})$ is a polynomial in $\log (2)$, $\pi$, Riemann zeta values, and Dirichlet beta va…