On a weighted sum of multiple T-values of fixed weight and depth

2020/12/21 by Yoshihiro Takeyama, Takeyama, Yoshihiro
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.11063

openalex publication_date 2020/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The multiple T-value, which is a variant of multiple zeta value of level two, is introduced by Kaneko and Tsumura. We show that the generating function of a weighted sum of the multiple T-values of fixed weight and depth is given in terms of the multiple T-values of depth one by solving a differential equation of Heun type.

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