Posts: 1,358

Threads: 330

Joined: Feb 2009

Posts: 631

Threads: 22

Joined: Oct 2008

(09/14/2010, 11:04 PM)mike3 Wrote: ... Not sure exactly what you'd want to know. It seems to be similar to the "Cauchy integral" for bases outside and in some parts of the STR, but the weird part is that when it is used for , it gives the attracting regular iteration. ???

This makes sense, in that I'm fairly certain that the attracting regular iteration is a 1-cyclic function of the entire regular superfunction.

http://math.eretrandre.org/tetrationforu...hp?tid=515 At least, it seems to be the case for base e^(1/e), and for sqrt(2). I'll half to read up on your post, to try to better understand your algorithm, (and ideally, your numerical approximations as well, and how you iteratively develop the solution).

- Sheldon

Posts: 368

Threads: 44

Joined: Sep 2009

(09/14/2010, 11:36 PM)sheldonison Wrote: This makes sense, in that I'm fairly certain that the attracting regular iteration is a 1-cyclic function of the entire regular superfunction. http://math.eretrandre.org/tetrationforu...hp?tid=515 At least, it seems to be the case for base e^(1/e), and for sqrt(2). I'll half to read up on your post, to try to better understand your algorithm, (and ideally, your numerical approximations as well, and how you iteratively develop the solution).

- Sheldon

I'll post the details of the numerical algorithm in the Computation forum, then.