11/21/2021, 06:37 AM
I thought I'd add another photo dump post. These are all of inverse Abel functions for \(e^{\mu z}\) with period \(2\pi i / \lambda\). These are all as hi res as I could; and also as convenient.
base \(\mu = 1\); multiplier \(\lambda = 0.25\):
base \(\mu = 0.3+i\); multiplier \(\lambda = 1\):
base \(\mu = 1+i\); multiplier \(\lambda = 1+i\):
And similarly: base\(\mu = 1+i\); multiplier \(\lambda=1\):
I believe I understand where and when Sheldon's gauntlet of zeroes appear; and when they appear they cause branch cuts; evident in pretty much all these photos.
base \(\mu = 1\); multiplier \(\lambda = 0.25\):
base \(\mu = 0.3+i\); multiplier \(\lambda = 1\):
base \(\mu = 1+i\); multiplier \(\lambda = 1+i\):
And similarly: base\(\mu = 1+i\); multiplier \(\lambda=1\):
I believe I understand where and when Sheldon's gauntlet of zeroes appear; and when they appear they cause branch cuts; evident in pretty much all these photos.