# Question on arguments of the Gamma Function

I came accross with this site about Gamma function. I just want to verify, clarify, whatever you may want to call it. It says you can compute for the gamma value for a negative argument using $$\Gamma(-z)=\frac{-\pi}{z\Gamma(z)\sin(\pi z)}$$

Is this true for all? I thought you cant have the negative numbers as argument for the gamma function.

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Indeed $\Gamma(-n)$ is not defined, for $n \in \Bbb N_{>0}$ (as is apparent from the $\sin(\pi z)$ factor in the denominator). Luckily, there are many more negative numbers than just the negative integers. –  Lord_Farin Oct 23 '12 at 6:26
Hi. thank you for that. Does it follow that $$\Gamma(z)=\frac{\pi}{z\Gamma(z)\sin(\pi z)},z>0,z\not\in\mathbb{Z}$$? Sorry for asking too many questions. Im just really having a tough time on my paper. Thanks again. –  Mynameis Tiara Oct 23 '12 at 6:43
Take a look at Euler's reflection formula. And while you're at it, there is much more information on the gamma function at the link. –  Harald Hanche-Olsen Oct 23 '12 at 7:33