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Optimal bounds for the generalized Euler-Mascheroni constant.

Ti-Ren Huang1, Bo-Wen Han1, Xiao-Yan Ma1

  • 11Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, China.

Journal of Inequalities and Applications
|May 29, 2018
PubMed
Summary
This summary is machine-generated.

This study establishes new upper and lower bounds for the generalized Euler-Mascheroni constant. These findings refine and improve existing bounds for the Euler-Mascheroni constant.

Keywords:
Asymptotic formulaEuler–Mascheroni constantgamma functionpsi function

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Area of Science:

  • Mathematics
  • Number Theory

Background:

  • The Euler-Mascheroni constant (γ) is a fundamental mathematical constant.
  • Generalized forms of constants are crucial for extending mathematical theories.

Purpose of the Study:

  • To derive sharp upper and lower bounds for the generalized Euler-Mascheroni constant.
  • To improve upon existing bounds for the Euler-Mascheroni constant.

Main Methods:

  • Analytical number theory techniques.
  • Derivation of inequalities.

Main Results:

  • Several new sharp upper and lower bounds for the generalized Euler-Mascheroni constant are presented.
  • The established bounds offer tighter estimations than previously known results.

Conclusions:

  • The derived bounds provide a more precise understanding of the generalized Euler-Mascheroni constant.
  • This work contributes to the ongoing refinement of bounds for important mathematical constants.