# Calculating Values for Reimann zeta function

I am trying to find values for $$z$$ in $$\zeta(z)$$. However I am tired of using the series:

$$\zeta(z)=\sum_{k=1}^\infty \frac{1}{k^z}$$

Is there any other method to find $$\zeta(z)$$ for $$Re(z)>1$$?

• Yes, there are many alternative representations of $\zeta$. One of the easiest to obtain directly from the "standard" series representation is the relationship to the $\eta$ function. And the standard series representation of $\eta$ is valid for $\text{Re}(z)>0$! – Mark Viola Mar 3 '18 at 18:31
• What do you mean by "find $z$ in $\zeta(z)?$" Do you want to compute the functional inverse $\zeta^{-1}(z)$ or just $\zeta(z)$ for $z>1?$ – gammatester Mar 3 '18 at 18:42