Further improvements of some double inequalities for bounding the gamma function

The aim of this paper is to establish some inequalities for bounding the gamma function that yields sharp asymptotic estimates for Γ(x) as x tends to ∞. Our results improve several known results stated by Alzer [H. Alzer, Inequalities for the gamma function, Proc. Amer. Math. Soc., 128 (1) (1999) 141-147], Andreson and Qiu [G.D. Anderson, S.-L. Qiu, A monotonicity property of the gamma function, Proc. Amer. Math. Soc., 125 (1997), 3355-3362], and Li and Chen [J. Choi, Some mathematical constants, Appl. Math. Comput., 187 (2007) 122-140].