Could someone confirm me the validity of the following formula:
$$\zeta\left(z\right)=2^{z}\pi^{z-1}\sin\left(\frac{\pi z}{2}\right)\left(\frac{e^{-\gamma \left(1-z\right)}}{1-z}\prod_{n=1}^{\infty}\frac{e^{\frac{1-z}{n}}}{1+\frac{1-z}{n}}\right)\zeta\left(1-z\right)$$
for the Riemann Zeta function accross the entire complex plane ?
EDIT: another non-related question: is the notation without parenthesis ambiguous for a mathematician? $$\zeta\left(z\right)=2^{z}\pi^{z-1}\sin\left(\frac{\pi z}{2}\right)\frac{e^{-\gamma \left(1-z\right)}}{1-z}\prod_{n=1}^{\infty}\frac{e^{\frac{1-z}{n}}}{1+\frac{1-z}{n}}\zeta\left(1-z\right)$$