z^^z ?

[bo198214]

I edited to change from "e" to "superE" on my post #5, sorry.

i dont know what your talking about actually.

There is this bifurcation base 1.6353... for the tetrational:

for b<1.6353... b[4]x has two fixpoints
for b=1.6353... b[4]x has one fixpoint
for b>1.6353... b[4]x has no fixpoint
on the positive real axis.

As you see, the bifurcation base 1.6353... of the tetrational corresponds to the bifurcation base \( e^{1/e} \) of the exponential.
(Also corresponds regarding other characterizations like the point b where b[4](b[4](b[4]...)) starts to diverge or the argument where the 4-selfroot is maximal)

The normal Euler constant e is now the one fixpoint of \( e^{1/e}[3]x \).
And the Super-Euler constant is the one (positive) fixpoint of \( 1.6353...[4]x \).