Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function

Journal of inequalities and applications

Shanhe Wu¹ 

关键词: DeTemple sequence;    convergence;    Euler-Mascheroni constant;    approximation;    Riemann zeta function;    41A60;    41A25;    57Q55;   

DOI  :  10.1186/s13660-017-1385-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce new sequences, which generalize the celebrated DeTemple sequence, having enhanced speed of convergence. We also give a new representation for Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers.

【 授权许可】

CC BY