Sums of infinite series involving the Riemann zeta function

被引：0

作者：

Mortini, Raymond ^{[1
,2
,3
]}

Rupp, Rudolf ^{[4
]}

机构：

[1] Univ Lorraine, Dept Math, CNRS, F-57000 Metz, France

[2] Univ Lorraine, Inst Elie Cartan de Lorraine, CNRS, F-57000 Metz, France

[3] Univ Luxembourg, Dept Math, L-4364 Esch Sur Alzette, Luxembourg

[4] TH Nurnberg, Fak Angew Math Phys & Allgemeinwissensch, Kesslerpl 12, D-90489 Nurnberg, Germany

来源：

ARCHIV DER MATHEMATIK | 2024年

关键词：

Riemann zeta function; Harmonic numbers; Alternating harmonic numbers; Cotangens;

D O I：

10.1007/s00013-024-02008-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the values of several infinite series involving the Riemann zeta function. In particular, degree one rationally weighted summands involving the Riemann function evaluated at even numbers give a finite sum involving only the Riemann function evaluated at odd numbers.

引用

页码：163 / 172

页数：10

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