The Euler-Riemann zeta function in some series formulae and its values at odd integer points

被引：0

作者：

Stevanovic, Milorad R. ^{[1
]}

Petrovic, Predrag B. ^{[1
]}

机构：

[1] Univ Kragujevac, Fac Tech Sci Cacak, Svetog Save 65, Cacak 32000, Serbia

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 180卷

关键词：

Riemann zeta function; Odd integer; Raabe's integral; Abel's criteria; Bernoulli numbers;

D O I：

10.1016/j.jnt.2017.05.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper presents formulae for certain series involving the Riemann zeta function. These formulae are generalizations, in a natural way, of well known formulae, originating from Leonhard Euler. Formulae that existed only for initial values n = 0,1 are now found for every natural n. Relevant connections with various known results are also pointed out. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：769 / 786

页数：18

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