Modified convergences to the Euler-Mascheroni constant
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Cristinel Mortici
cristinel.mortici@valahia.ro
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https://doi.org/10.56754/0719-0646.2801.043Abstract
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.
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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.
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