Chapter 11.5, Problem 5P

Use (5.4) to show that

(a) $\Gamma \left(\frac{1}{2}-n\right)\Gamma \left(\frac{1}{2}+n\right)={(-1)}^n\pi$ if $n=$ a positive integer;

(b) $(z!)(-z)!=\pi z/\sin \pi z,$ where $z$ is not necessarily an integer; see comment after equation (3.3).