Slog(Exponential Factorial(x))

[tommy1729]

Paulsen and Cowgill's paper is a mathematical paper, which constructs Kneser, and gives a uniqueness condition for Kneser. They don't really make an algorithm, per se, just explain how to grab Taylor series and calculate them. Which, I guess, is an algorithm in and of itself.

http://myweb.astate.edu/wpaulsen/tetration2.pdf

It's a fantastic paper. Paulsen has another paper exploring complex bases, but I think it lacks a good amount of the umph! of this paper, lol. It's not too hard to read, and in my mind, is a very cogent explanation of Kneser.


Also, I just have an irrational hatred of matrices. Not even that it's particularly hard, I can still use matrices if pressed--I just hate them. Lol I'm matrix phobic, lol.

Im still left with many many questions.

anyways,
I had the vague idea of mapping a boundary R to the real line iteratively.

that is to say by some kind of averaging.

by analogue when you want to map f(x) to the zero function you do something like 

f(x)/2

f(x)/2 /2 

f(x) /2 /2 /2

and 

g1(f(x)) = f(x)/2

g2(g1(f(x))) = f(x)/4

etc

the sequence g_n are bounded functions that get weaker and weaker ( closer to id(z)) , so the sequence g_n(g_{n-1}(... )  is analytic.

maybe this is a garbage idea but it seems intuitive to me.

In fact , what do we know about fractional (iterations of) riemann mappings ?

In essense they are just fractional iterations of analytic functions but still ... I feel we might be missing something here.


regards

tommy1729