Modified convergences to the Euler-Mascheroni constant

Cristinel Mortici

doi:10.56754/0719-0646.2801.043

Authors

Cristinel Mortici Academy of Romanian Scientists, Strada IIfov nr. 3, 050044 Bucureşti, Romania – Department of Science and Advanced Technologies, Faculty of Sciences and Arts, Valahia University of Târgovişte, Aleea Sinaia 13, 130004 Târgovişte, Romania – National University of Science and Technology Politehnica Bucureşti, Splaiul Independenţei 313, 060042 Bucureşti, Romania. https://orcid.org/0000-0001-5576-1921

DOI:

https://doi.org/10.56754/0719-0646.2801.043

Keywords:

Euler-Mascheroni constant, Euler’s gamma function, digamma function, approximations, speed of convergence

Abstract

We introduce in this paper some new sequences that converge to the Euler-Mascheroni constant. These sequences have a higher convergence rate than the classical one. Further properties are given.

Downloads

Download data is not yet available.

References

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, ser. National Bureau of Standards Applied Mathematics Series. U. S. Government Printing Office, Washington, DC, 1964, vol. 55.

C.-P. Chen and C. Mortici, “Approximations of the harmonic numbers,” Results Math., vol. 80, no. 1, 2025, Art ID. 35, doi: 10.1007/s00025-025-02355-z.

J. Feng, D. Lu, and Z. Wen, “Some new sequences and inequalities related to Euler’s constant,” Results Math., vol. 73, no. 4, 2018, Art ID. 158, doi: 10.1007/s00025-018-0919-1.

I. R. Harris, “A family of sequences which converge to the Euler-Mascheroni constant,” Carpathian J. Math., vol. 40, no. 1, pp. 37–45, 2024.

C. Mortici, “Fast convergences towards Euler-Mascheroni constant,” Comput. Appl. Math., vol. 29, no. 3, pp. 479–491, 2010, doi: 10.1590/S1807-03022010000300009.

C. Mortici, “Product approximations via asymptotic integration,” Amer. Math. Monthly, vol. 117, no. 5, pp. 434–441, 2010, doi: 10.4169/000298910X485950.