Improving some inequalities associated with the Euler-Mascheroni constant
نویسندگان
چکیده
منابع مشابه
Limits and inequalities associated with the Euler-Mascheroni constant
(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 int...
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Let Rn = n k=1 1 k −log n + 1 2 , H(n) = n 2 (Rn −γ), n = 1, 2,. . ., where γ is the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, H(n) and [(n + 1/2)/n] 2 H(n) are strictly increasing, while [(n + 1)/n] 2 H(n) is strictly decreasing. For all integers n ≥ 1, 1 24(n + a) 2 ≤ Rn − γ < 1 24(n + b) 2 with the best possible constants a = 1 24[−γ + 1 − log(3/2)] − 1 = 0.55106. .. a...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2019
ISSN: 1846-579X
DOI: 10.7153/jmi-2019-13-44