Abstract
The aim of this paper is to establish some new continued fraction inequalities for the Euler-Mascheroni constant by multiple-correction method.
Highlights
Euler introduced a constant, later this constant was called ‘Euler’s constant’ as the limit of the sequence n γ (n) := – ln n. ( . ) m m=It is known as the Euler-Mascheroni constant
Many authors are preoccupied to improve its rate of convergence, see e.g. [, – ] and the references therein
In this paper, starting from the sequence ν(n), based one the works of Mortici, Chen and Lu, we provide some new classes of convergent sequences with faster rate of convergence for the Euler-Mascheroni constant as follows
Summary
Abstract The aim of this paper is to establish some new continued fraction inequalities for the Euler-Mascheroni constant by multiple-correction method. It is known as the Euler-Mascheroni constant. The sequence (γ (n))n∈N converges very slowly toward γ , like ( n)– , by Young (see [ ]). Many authors are preoccupied to improve its rate of convergence, see e.g. Mortici and Chen [ ] provided a very interesting sequence n ν(n) =
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