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Symmetric Tornheim double zeta functions
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ( IF 0.4 ) Pub Date : 2021-02-09 , DOI: 10.1007/s12188-021-00232-4 Takashi Nakamura
中文翻译:
对称的Tornheim双Zeta函数
更新日期:2021-02-09
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ( IF 0.4 ) Pub Date : 2021-02-09 , DOI: 10.1007/s12188-021-00232-4 Takashi Nakamura
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.
中文翻译:
对称的Tornheim双Zeta函数
令\ {s,t,u \ in {{\ mathbb {C}}} \}和T(s, t, u)为Tornheim double zeta函数。在本文中,我们研究了对称的Tornheim双zeta函数的一些性质,这些特性可以看作Tornheim双zeta函数的奇异化。作为推论,我们根据γ函数和黎曼zeta函数的级数给出了T(s, t, u)的显式评估公式或快速收敛的级数表示。