A Trigonometric Variant of Kaneko–Tsumura ψ -Values

Ende Pan, Xin Lin, Ce Xu and Jianqiang Zhao ()
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Ende Pan: College of Teacher Education, Quzhou University, Quzhou 324022, China
Xin Lin: School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China
Ce Xu: School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China
Jianqiang Zhao: Department of Mathematics, The Bishop’s School, La Jolla, CA 92037, USA

Mathematics, 2024, vol. 12, issue 23, 1-14

Abstract: 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.

Keywords: trigonometric-variant; Kaneko–Tsumura ? -function; (alternating) multiple T -values; iterated integrals; duality formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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