Sat, 14 Sep 2019
[ (Previously) ]
Wikipedia has an animation that shows the convergence of the Maclaurin series for the exponential function:
This makes it look a lot better-behaved than it is. First, because it only shows a narrow region around the center of convergence. But also, it emphasizes the right-hand quadrant, where the convergence is monotone.
If you focus on the left-hand side instead, you see the appoximations thrashing back and forth like a screen door in a hurricane:
This is the same as Wikipedia's animation, just focused on a slightly different region of the plane. But how different it looks!