Gamma(-1/2) proof

1. What is the gamma function of (- 1 2?
2. How is gamma 1 2 equal to root pi proof?

What is the gamma function of (- 1 2?

The key is that Γ(1/2)=√π.

How is gamma 1 2 equal to root pi proof?

We use Euler's Reflection Formula Γ(1−z)Γ(z)=πsin(πz) with z=12. We then have Γ(1/2)2=πsin(π2). Since sin(π2)=1 we now have Γ(1/2)2=π. Finally therefore Γ(1/2)=√π.