A more accurate approximation for the gamma function

In this paper, we establish a double inequality for the gamma function, from which we deduce the following approximation formula:Γ(x+1)∼2πx(xe)x(1+112x3+247x−12)x2+53210,x→∞, which is more accurate than the Burnside, Gosper, Ramanujan, Windschitl, and Nemes formulas. We develop the previous approximation formula to produce an asymptotic expansion.