A Trigonometric Variant of Kaneko–Tsumura ψ-Values

Many variations of the multiple zeta values have been found to play important roles in different branches of mathematics and theoretical physics in recent years, such as the cyclotomic/color version, which appears prominently in the computation of Feynman integrals. In this paper, we introduce a trigonometric variant of the Kaneko–Tsumura ψ-function (called the Kaneko–Tsumura ψ˜-function) and discover some nice properties similar to those for ordinary Kaneko–Tsumura ψ-values using the method of iterated integrals, which was first studied systematically by K.T. Chen in the 1960s. In particular, we establish some duality formulas involving the Kaneko–Tsumura ψ˜-function and alternating multiple T-values by adapting Yamamoto’s graphical representation method for computing special types of iterated integrals.