For example if you look at this graph the real and imaginary parts along the critical line $x$ is plugged into what equation? It can't be the normal function:
$$\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^{s}}$$
my understanding is that that is divergent in the critical strip. I know enough to know that you have to analytically continue the normal function, but reading all this different stuff there's all kinds a weird series and confusion. Perhaps I don't know enough to even ask my question, but for them to have plotted that graph up there don't they have some functions to plug x into? So for example was it this one?
or is it this?
or perhaps it was this guy:
Do you see what I'm saying? Where's the y=f(x) versions that make those plots of zeta going to zero along re=1/2? I feel like knowing how to plot that would help me understand the Riemann hypothesis a little better.