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Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function.
1Department of Mathematics, Longyan University, Longyan, Fujian 364012 P.R. China.
Journal of Inequalities and Applications
|May 30, 2017
Summary
Researchers developed new DeTemple sequences with faster convergence rates. A novel representation for Euler
Area of Science:
- Number Theory
- Mathematical Analysis
Background:
- The DeTemple sequence is a known method for approximating mathematical constants.
- Euler's constant (γ) is a fundamental mathematical constant with various representations.
Purpose of the Study:
- To introduce novel sequences generalizing the DeTemple sequence.
- To enhance the speed of convergence for these sequences.
- To present a new representation for Euler's constant.
Main Methods:
- Generalization of the DeTemple sequence.
- Analysis of convergence rates.
- Utilizing the Riemann zeta function at positive odd integers.
Main Results:
- Introduction of new, faster-converging sequences.
- A novel mathematical formula for Euler's constant.
- Demonstration of the relationship between the new sequences and Euler's constant.
Conclusions:
- The newly developed sequences offer improved computational efficiency.
- The new representation provides deeper insight into Euler's constant and its relation to the Riemann zeta function.
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