Complex Gamma? - 2

$\Gamma(n)\approx\sqrt{2\pi(n-1)}\left(\dfrac{n-1}{e}\right)^{n-1}$ We want a very big n for good approximation. pi is small. for about 3 decimal places of accuracy 1000 is enough. so $\Gamma(1001+\pi)=\Gamma(\pi)\prod_{i=0}^{1000} (\pi+i)\approx\sqrt{2\pi(\pi+1000)}\left(\dfrac{\pi+1000}{e}\right)^{\pi+1000}\\ \Gamma(\pi)\approx\sqrt{2\pi(\pi+1000)}\left(\dfrac{\pi+1000}{e}\right)^{\pi+1000}\prod_{i=0}^{1000} \dfrac{1}{\pi+i}\approx \boxed{2.288}$