Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(5): 1261-1278

Online first article August 26, 2021      Printed September 30, 2021

https://doi.org/10.4134/BKMS.b200933

Copyright © The Korean Mathematical Society.

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

Ce Xu

Anhui Normal University

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.

Keywords: Kaneko-Tsumura multiple $T$-values, alternating multiple $T$-values, weighted sum formulas, duality

MSC numbers: Primary 11M99, 11M06, 11M32

Supported by: The author is supported by the Scientific Research Foundation for Scholars of Anhui Normal University and the University Natural Science Research Project of Anhui Province (Grant No. KJ2020A0057).

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