Theory about tetrating bases from 0 to e^-e via the continuum sum
#2
(12/10/2009, 02:30 AM)mike3 Wrote: What do you think of my theory?

Hm, well, for me it sounds quite "constructed".
I think you should point out what criteria your super-exponential should satisfy.
I mean we have already a solution (see the predecessor thread) but somehow you dont find it satisfactory. So what kind of solution do you want? Please specify!

Quote: Also, can you give a graph of the regular superexponential of such a base developed the repelling real fixed point? Even though it's not the tetrational we want, it might nonetheless help to get a general idea of what the behavior may be like. Helms posted a graph for \( b = 0.04 \) once, but it was a parametric plot, not a plot along the x-axis.

What plot do you want? He posted the super-exponential \( f(x)={\exp_{0.04}}^{\circ x}(0.5) \) for real \( x \).


Messages In This Thread
RE: Theory about tetrating bases from 0 to e^-e via the continuum sum - by bo198214 - 12/10/2009, 02:06 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  [UFO] "commutative number theory " f(g) = g(f) tommy1729 0 408 03/24/2023, 11:36 PM
Last Post: tommy1729
  double functional equation , continuum sum and analytic continuation tommy1729 6 1,770 03/05/2023, 12:36 AM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 8 15,967 02/08/2023, 03:49 AM
Last Post: JmsNxn
  geometric function theory ideas tommy1729 0 584 12/31/2022, 12:19 AM
Last Post: tommy1729
Question Convergent Complex Tetration Bases With the Most and Least Imaginary Parts Catullus 0 803 07/10/2022, 06:22 AM
Last Post: Catullus
  Tetration extension for bases between 1 and eta dantheman163 23 43,983 07/05/2022, 04:10 PM
Last Post: Leo.W
  " x-theory " tommy1729 1 1,767 08/12/2021, 12:17 AM
Last Post: tommy1729
  Dynamical Systems and Number Theory Daniel 4 3,924 06/01/2021, 11:34 PM
Last Post: JmsNxn
  Set theory debate : cantor 1st / Virgil argument. tommy1729 1 5,211 12/08/2015, 11:14 PM
Last Post: tommy1729
  2015 Continuum sum conjecture tommy1729 3 8,839 05/26/2015, 12:24 PM
Last Post: tommy1729



Users browsing this thread: 2 Guest(s)