## Wonder how to evaluate this factorial (−12)!\left(-\frac{1}{2}\right)!

I’ve learned factorial. But today I saw a question which I don’t know how to start with: (−12)! Can anyone explain how to solve it? Thanks Answer As suggested by Workaholic, I=(−12)!=Γ(12)=∫+∞0x−1/2e−xdx=2∫+∞0e−y2dy=∫Re−y2dy and by Fubini’s theorem: I2=∫R2e−(y2+z2)dydz=∫2π0∫+∞0ρe−ρ2dρdθ=π∫+∞02ρe−ρ2dρ=π so: (−12)!=√π. AttributionSource : Link , Question Author : Mathxx , Answer Author : Jack D’Aurizio