Work

A Trigonometric Variant of Kaneko–Tsumura ψ-Values

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12233771

Authors: Ende Pan, Xin Lin, Ce Xu, Jianqiang Zhao

Institutions: Quzhou University, Anhui Normal University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: National Natural Science Foundation of China, Natural Science Foundation of Anhui Province, University Natural Science Research Project of Anhui Province