# Gamma function

1. Feb 6, 2012

### Ted123

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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 $n<0$ ?

2. Feb 6, 2012

### vela

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