Limits and inequalities associated with the Euler-Mascheroni constant

Abstract

(i) We present several limits associated with the Euler-Mascheroni constant. (ii) Let γ = 0.577215 . . . be the Euler-Mascheroni constant, and let Tn = ∑n k=1 1 k − ln ( n+ 1 2 + 1 24n ) and Pn = ∑n k=1 2 2k−1 − ln(4n). We determine the best possible constants α, β, a and b such that the inequalities 1 48(n+ α)3 ≤ γ − Tn < 1 48(n+ β)3 and 1 24(n+ a)2 ≤ Pn − γ < 1 24(n+ b)2 are valid for all integers n ≥ 1.

DOI: 10.1016/j.amc.2013.03.089

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Cite this paper

@article{Chen2013LimitsAI, title={Limits and inequalities associated with the Euler-Mascheroni constant}, author={Chao-Ping Chen and Cristinel Mortici}, journal={Applied Mathematics and Computation}, year={2013}, volume={219}, pages={9755-9761} }