multiplication formula for gamma function

For any integer $n>0$, the gamma function satisfes the following relation:

$$\mathrm{\Gamma }(nz)={(2\pi )}^{\frac{n-1}{2}}{n}^{nz-\frac{1}{2}}\prod _{k=0}^{n-1}\mathrm{\Gamma }\left(z+\frac{k}{n}\right)$$

This equation is true for all complex values of $z$ for which both sides are defined.