02/27/2011, 11:01 PM

(02/27/2011, 12:55 PM)bo198214 Wrote:(01/30/2011, 06:41 PM)tommy1729 Wrote:(01/29/2011, 11:18 PM)nuninho1980 Wrote: 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 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 .

And the Super-Euler constant is the one (positive) fixpoint of .

i suppose - without thinking about it - there is a fast converging method to find 1.6353... which also shows its transcendental.

i dont have much time to explore it nowadays ...