A new asymptotic series for the Gamma function

The famous Stirling's formula says that Γ(s+1)=2πs(s/e)seγ(s)=2π(s/e)seθ(s)/12s. In this paper, we obtain a novel convergent asymptotic series of γ(s)γ(s) and proved that θ(s)θ(s) is increasing for s>0s>0.