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 wrong.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

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 wrong.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