Gamma function (infinite product representation)

[math8]

I have come across this expression in some notes

\Gamma (z) = \frac{1}{z} \prod \frac{(1+ \frac{1}{n})^{z}}{1+ \frac{z}{n}}

Do you think it's accurate? I have some doubts because I have looked for it on wokipedia, and I couldn't find it.

 

[gabbagabbahey]

Do you mean

\Gamma(z)=\frac{1}{z}\prod_{n=1}^{\infty} \frac{\left(1+\frac{1}{n}\right)^z}{1+\frac{z}{n}}

If so, then yes, it's correct for all complex numbers z except for zero and negative integers.

 

[math8]

Thanks a lot :)