# Gamma function (infinite product representation)

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
Homework Helper
Gold Member
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.

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Thanks a lot :)