As part of my tutorial, I would like to show the plots of a)$-\sum_{n\geq 1}\frac{1}{n}z^{n}$ and b)$Log(1-z)=log(|z|)+iArg(z)$, to drive home the point of analytic continuation.
Plotting the Log is easy but not the power series. Any suggestions for Matlab, mathematica or c++?
So far I've been trying with the symbolic sum function, but it was too heavy for my machine. I might leave it for few hours to run.
Any quicker ways?
Specifically I want to plot $\sum_{n\geq 1}\frac{1}{n}r^{n}cos(n\theta)$ and $\sum_{n\geq 1}\frac{1}{n}r^{n}sin(n\theta)$ separately.
Here is a graph of a natural boundary image I found online. 