Duality of Weighted Sum Formulas of Alternating Multiple $T$-Values

Abstract

Recently, a new kind of multiple zeta value level two $T(\mathbf{k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple $T$-values, and study several duality formulas of weighted sum formulas about alternating multiple $T$-values by using the methods of iterated integral representations and series representations. Some special values of alternating multiple $T$-values can also be obtained.

References in corpus (2)

• On Multiple Zeta Values of Even Arguments
• Alternating Euler $T$-sums and Euler $\tilde{S}$-sums

Cited by in corpus (1)

• Evaluation of multivariate integrals based on a duality identity for the Stieltjes transform