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

Abstract

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.

Keywords

• DeTemple sequence
• convergence
• Euler-Mascheroni constant
• approximation
• Riemann zeta function