• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 iterating exp(z) + z/(1 + exp(z)) tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 07/17/2020, 12:29 PM I come back to an old idea. The issue with iterating is exp is that it's inverse is not real for negative real imput. So I considered iterating exp(x) + x which has no finite fixpoint. There is a thread about that. BUT a better asymptotic to a linear function for negative x and exp for positive x is the simple  exp(z) + z/(1 + exp(z)) It also has a closed form inverse and two fixpoints who can also be given in closed form. That closed forms requires lambertW. More methods will work here too. But my main question is how its super/abel/semi-iterate etc behave and look on the complex plane. How different it is from iterations of exp , dexp or 2sinh. And - more advanced - how the super of the super differs from pentation. I prefer the abel function to be completely monotone beyond a certain real value y. ( as i do for slog btw , still no solution as far as i know ??? ) Iterating this functions feels natural too me ! Regards Tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post iterating x + ln(x) starting from 2 tommy1729 2 5,008 04/29/2013, 11:35 PM Last Post: tommy1729 iterating non-analytic tommy1729 0 3,108 02/08/2011, 01:25 PM Last Post: tommy1729 Iterating at fixed points of b^x bo198214 28 40,803 05/28/2008, 07:37 AM Last Post: Kouznetsov

Users browsing this thread: 1 Guest(s)