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.