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$a\\in (0, \\infty)$, $\\gamma(a)$ be the Generalized Euler-Mascheroni Constant, and let \\begin{align*} &x_n=\\frac1a+\\frac{1}{a+1}+\\cdots+\\frac{1}{a+n-1}-\\ln\\frac{a+n}{a},\\\\ &y_n=\\frac1a+\\frac{1}{a+1}+\\cdots+\\frac{1}{a+n-1}-\\ln\\frac{a+n-1}{a}. \\end{align*} In this paper, we determine the best possible constants $\\alpha_i, \\beta_i (i=1,2,3,4)$ such that the following inequalities \\begin{align*} \\frac{1}{2(n+a)-\\alpha_1}\\leq &\\gamma(a)-x_n< \\frac{1}{2(n+a)-\\beta_1},\\\\ \\frac{1}{2(n+a)-\\alpha_2}\\leq &y_n-\\gamma(a)< \\frac{1}{2(n+a)-\\beta_2},\\\\ \\frac{1}{2(n+a)}+\\frac{\\alpha_3}{(n+a)^2}\\leq &\\gamma(","authors_text":"Bo-Wen Han, Ti-Ren Huang, Xiao-Yan Ma, You-Ling Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-23T16:19:12Z","title":"Sharp Estimates of the Generalized Euler-Mascheroni 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