07/01/2019, 12:11 PM
(This post was last modified: 07/11/2019, 01:37 PM by Ember Edison.)

I have been reading post in forum for two weeks. Now I feel I was too young, too simple, and naive for tetration.

I need somebody to help me clarifiy the elementary knowledge for tetration.

My understanding of the tetration is:

I need somebody to help me clarifiy the elementary knowledge for tetration.

My understanding of the tetration is:

Quote:Code definition:

=ComplexInfinity (infinite magnitude, undetermined complex phase)

Not consider the branch cut:

and:

and:

is oscillates infinitely, but maybe 0 and 1 are different branch of the infinite iterated exponential.

in other bases:

tetration, super-root and super-logarithm is infinitely differentiable. (but I wasn't find code take the derivative...)

If the bases is hyperbolic, there is only one "regular" super-function. If the bases is parabolic, will have at least 2 "regular" super-function.(Leau-Fatou-flower)

The branch cut for super-function is infinitely.

fatou.gp will use all "regular" super-function to refactoring tetration.

bases regions for tetration:

, Andrew Robbins

base=0, not supported

, unknown

, Koenig, no code

base=1, Andrew Robbins

, Koenig, fatou.gp

, Ecalle, fatou.gp

ill-region for Fatou.

other, Fatou, fatou.gp