Explicit evaluations for several variants of Euler sums

Abstract

We study several variants of Euler sums by using the methods of contour integration and the residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a variant of multiple zeta values of level 2, and we give some identities on relations between these variants of Euler sums and the variant of multiple zeta values.