Abstract
We provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant. As consequences, some previous bounds for the Euler–Mascheroni constant are improved.
Highlights
We clearly see that the generalized Euler–Mascheroni constant γ (a) is the natural generalization of the classical Euler–Mascheroni constant [2,3,4,5]
2 Main results In order to prove our main results, we need several formulas and lemmas which we present
N the generalized Euler–Mascheroni constant is defined by γ (a) = lim a+n–1 – log n→∞ a a + 1 a+n–1 a for a > 0
Summary
Chen [14] proved that α = 1/ 12γ – 6 – 1 and β = 0 are the best possible constants such that the double inequality The main purpose of this article is to find the best possible constants α1, α2, α3, α4, β1, β2, β3 and β4 such that the double inequalities
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