Expressing $\Gamma$(n+$\frac{1}{2}$) for n $\in$ $\mathbb{Z}$ in Factorials

[Ted123]

Homework Statement

Express \Gamma (n+\frac{1}{2}) for n\in\mathbb{Z} in terms of factorials (separately for positive and negative n).

Homework Equations

The Attempt at a Solution

I've got for n\geqslant 0 that \displaystyle \Gamma \left(n+\frac{1}{2} \right) = \frac{(2n-1)!}{2^n} \sqrt{\pi} but what do I do when n<0 ?

 

[vela]

The same thing. Use $n\Gamma(n)=\Gamma(n+1)$, so $(-1/2)\Gamma(-1/2) = \Gamma(1/2)$ and so on.