An accurate approximation formula for gamma function

In this paper, we present a very accurate approximation for the gamma function: G(x+1)similar to root 2 pi x(x/e)(x()xsinh1/x)(x/2)exp(7/324 1/x(3(35)x(2)+33))=W-2 (X) as x infinity, and we prove that the function x -> In Gamma(x+ 1) - In W-2(x) is strictly decreasing and convex from (1, infinity) onto (0,beta), where beta=22,025/22,032 - In root 2 pi sinh 1 approximate to 0.00002407.