09/28/2021, 04:41 PM
(This post was last modified: 09/28/2021, 04:45 PM by Ember Edison.)
(09/25/2021, 03:00 AM)JmsNxn Wrote: See my thread here; I run a quick toy model for a \( 2 \pi i \) periodic tetration base \( b = 1/2 \). As far as I can tell this should work on the real positive line; and should work in the complex plane, but I'm not sure. I think the real trouble would be \( b <0 \).
I will not be as optimistic as you are. The real big trouble should be b=\( e^{-e} \)≈0.065988035845312537076790187596846424938577048252796
If you really want to give yourself some real meaningful trials, try deriving a numerical approximation of the tetration function for the following bases:
b=e^-e, b=10^-10(, b=-10^-10), b=1+10^-10, b=1-10^-10(, b=1+10^-10 * I)
Oh, Maybe the numerical approximation accuracy you already have is not up to 10^-10, so you can try from 10^-5.
Maybe a simpler sequence would be b=0.1, 0.07, 0.066, 0.06599