What is $0.5!×(-0.5)!$?

Question

Based on the answers and help given, as$$ 0.5!= \sqrt{π}, \quad (-0.5)!= \sqrt{π}, $$ thus the product is $π$. Is this correct?

Answer 1

If one interprets $x!$ as $\Gamma(x+1)$ where $\Gamma$ denotes the Gamma function, then $(-1/2)!=\Gamma(1/2)=\sqrt\pi$ and $(1/2)!=\Gamma(3/2)=\sqrt\pi/2$. Therefore $$(-1/2)!(1/2)!=\frac\pi2.$$