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ON A WEIGHTED SUM OF MULTIPLE $\mathbf{{T}}$
-VALUES OF FIXED WEIGHT AND DEPTH
Published online by Cambridge University Press: 19 March 2021
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 3 , December 2021 , pp. 398 - 405
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
Footnotes
This work was partially supported by JSPS KAKENHI grant number 18K03233.
References
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