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

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

Abstract 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.

Bibliographic Details
Main Authors: Shanhe Wu, Gabriel Bercu
Format: Article
Language:English
Published: SpringerOpen 2017-05-01
Series:Journal of Inequalities and Applications
Subjects:
DeTemple sequence
convergence
Euler-Mascheroni constant
approximation
Riemann zeta function
Online Access:http://link.springer.com/article/10.1186/s13660-017-1385-0

Internet

http://link.springer.com/article/10.1186/s13660-017-1385-0

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