Explicit Relations Between Kaneko-Yamamoto Type Multiple Zeta Values and Related Variants

Abstract

In this paper we first establish several integral identities involving the multiple polylogarithm functions and the Kaneko-Tsumura A-function, which can be thought as a single-variable multiple polylogarithm function of level two. We find that these integrals can be expressed in terms of multiple zeta (star) values, their related variants (multiple tvalues, multiple T -values, multiple S-values, etc.), and multiple harmonic (star) sums and their related variants (multiple T -harmonic sums, multiple S-harmonic sums, etc.), which are closely related to some special types of Schur multiple zeta values and their generalizations. Using these integral identities, we prove many explicit evaluations of Kaneko-Yamamoto multiple zeta values and their related variants. Further, we derive some relations involving multiple zeta (star) values and their related variants.