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I need somebody to help me clarifiy the elementary knowledge for tetration
#1
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:

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
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Messages In This Thread
I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/01/2019, 12:11 PM

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