The multiple T-value, which is a variant of the multiple zeta value of level two, was introduced by Kaneko and Tsumura [‘Zeta functions connecting multiple zeta values and poly-Bernoulli numbers’, in: Various Aspects of Multiple Zeta Functions, Advanced Studies in Pure Mathematics, 84 (Mathematical Society of Japan, Tokyo, 2020), 181–204]. We show that the generating function of a weighted sum of 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.

中文翻译：

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关于固定权重和深度的多个值的加权和

多重吨-value 是第二级多重 zeta 值的变体，由 Kaneko 和 Tsumura 引入 ['连接多个 zeta 值和多伯努利数的 Zeta 函数'，在：多个 Zeta 函数的各个方面, 纯数学高级研究, 84 (日本数学会, 东京, 2020), 181–204]。我们证明了多个加权和的生成函数吨- 固定权重和深度的值以倍数给出吨-通过求解 Heun 类型的微分方程得到深度一的值。