THE RIEMANN ZETA FUNCTION AND CLASSES OF INFINITE SERIES

Applicable Analysis and Discrete Mathematics

article

Horst Alzer¹  Junesang Choi² 

[1] Morsbacher Str. 10;Department of Mathematics, Dongguk University

关键词: mathematical constants;    generalized (or Hurwitz) zeta function;    gamma;    digamma and polygamma functions;    Riemann zeta function;    Infinite series;   

DOI  :  10.2298/AADM1702386A

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We present one-parameter series representations for the following series involving the Riemann zeta functionX∞n=3n oddζ(n)nsnand X∞n=2n evenζ(n)nsnand we apply our results to obtain new representations for some mathematical constants such as the Euler (or Euler-Mascheroni) constant, the Catalanconstant, log 2, ζ(3) and π.

【 授权许可】

Unknown