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Duality of weighted sum formulas of alternating multiple $T$-values

Ce Xu
대한수학회 (The Korean Mathematical Society)|2021.09|대한수학회보 (Bulletin of the KMS)|제58권 제5호|pp. 1261-1278|DOI 10.4134/BKMS.b200933

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키워드

dualityKaneko-Tsumura multiple $T$-valuesalternating multiple $T$-valuesweighted sum formulas
주제분류수학

초록

Recently, a new kind of multiple zeta value of level two $T({\bf k})$ (which is called multiple $T$-value) 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.

Abstract

Recently, a new kind of multiple zeta value of level two $T({\bf k})$ (which is called multiple $T$-value) 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.

참고문헌 (24)

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