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complex iteration (complex "height")
#20
Some complex value tetration:

If I have understood right (if not, tell me please) , basic idea to be able to have some analytics relations is to make or

and if we have chosen complex or real then we can find such that :



So every time



E.g.

lower fixed point
we get the base by
if then



but :









this seems to equal 1. So with Imaginary height:



Few more interesting outcome :






Which seems wrongSad.So where all others, then...

Or actually a=e and base seems to be rather unique point in selfroots as it is the only one for a>1 which has only 1 value, so h(e^(1/e))=e and that is the only value ( all other points for a>1 has 2 values for h(a^(1/a))), because 2 different a on different sides of a=e have the same selfroot values).

So if we speculate a little to continue with 2 values as a demand for , we may propose that:










Or, if








But it was good tex training...

Ivars
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