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A new sequence convergent to Euler-Mascheroni constant.

Xu You1, Di-Rong Chen2

  • 11Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing, P.R. China.

Journal of Inequalities and Applications
|April 17, 2018
PubMed
Summary
This summary is machine-generated.

Researchers introduce a novel sequence that converges to the Euler-Mascheroni constant. This new sequence is then used to derive several inequalities for this important mathematical constant.

Keywords:
Euler–Mascheroni constantHarmonic sequenceRate of convergenceTaylor’s formula

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Area of Science:

  • Mathematics
  • Number Theory
  • Analysis

Background:

  • The Euler-Mascheroni constant (γ) is a fundamental mathematical constant.
  • Its properties and convergence rates are of significant interest in number theory and analysis.
  • Existing sequences for approximating γ have varying convergence behaviors.

Purpose of the Study:

  • To introduce a new sequence that converges to the Euler-Mascheroni constant.
  • To establish new inequalities involving the Euler-Mascheroni constant.
  • To contribute to the understanding of the approximation of γ.

Main Methods:

  • Construction of a novel infinite sequence.
  • Analysis of the convergence properties of the new sequence.
  • Derivation of inequalities using the established convergence.

Main Results:

  • A new sequence converging to the Euler-Mascheroni constant is presented.
  • Several new inequalities for the Euler-Mascheroni constant have been established.
  • The convergence rate of the new sequence is implicitly characterized through the inequalities.

Conclusions:

  • The paper successfully introduces a new sequence for approximating the Euler-Mascheroni constant.
  • The derived inequalities offer novel insights into the behavior of γ.
  • This work provides a new tool for studying the Euler-Mascheroni constant.