Symmetric Tornheim double zeta functions

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-02-09 DOI:10.1007/s12188-021-00232-4

Takashi Nakamura

引用次数: 3

Abstract

Let \(s,t,u \in {{\mathbb {C}}}\) and T(s, t, u) be the Tornheim double zeta function. In this paper, we investigate some properties of symmetric Tornheim double zeta functions which can be regarded as a desingularization of the Tornheim double zeta function. As a corollary, we give explicit evaluation formulas or rapidly convergent series representations for T(s, t, u) in terms of series of the gamma function and the Riemann zeta function.

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对称Tornheim双ζ函数

设\(s,t,u \in {{\mathbb {C}}}\)和T(s, T, u)为Tornheim的二重函数。本文研究了对称Tornheim二重zeta函数的一些性质，这些性质可以看作是对Tornheim二重zeta函数的一种非具体化。作为推论，我们给出了T(s, T, u)用函数和黎曼函数的级数表示的显式计算公式或快速收敛的级数表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.