Real tetration as a limit of complex tetration

[Daniel]

I agree with Daniel.

I had similar ideas in the past.
I made a post somewhere I am sure of that.


The thing is this :

If the derivative at the fixpoint has small imaginary value the angular rotation is small.

So if the fixpoint is also far away , combined with bounded angular rotation , we get almost no rotation.

The rotation converges to zero if the distance to the fixpoint converges to infinity and we pick a subset that has small angular rotation ( aka imag part of the derivative ).

So the question is ; is it justified to take that limit ?? 

Does that converge properly to a unique and analytic function ?

I am not sure any of this or a variant is even justified but it is worth investigating.



regards

tommy1729

I'm first trying to develop a mental picture of the problem so that I have something to look for when I model the problem. Plus we now have Paulsen's JavaScript calculator, which I believe gives valid results for expressions like \(^{.5}2\). Next I need to analyze the values of an expression like \(^{.5}2\) that are associated to the different fixed points.