A new asymptotic series for the Gamma function

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