(12/26/2009, 01:44 AM)sheldonison Wrote: Great plots, thanks. Do you use "mathematica"? The only tools I'm using are excel, and "perl".
I like the "eta" plot. I've plotted some of the n*e*pi contour lines of eta in the complex plane, which all iterate to i=0 contour lines, and which seem to be the defining features of the eta graph, along with the real=e contour lines. I'll probably post some time.
The two functions seem like they should be assymptotic on real number line, but its a ringing pattern. If you shift them so that they're super-exponential growth lines up, by taking sexp_eta(x+0.584) and sexp_e(x), the two graphs will intersect each other an infinite number of times, as they both super-exponentially climb to infinity, each on a slightly different pattern.
- Shel
The calculation was done using the Pari/GP package, with a hand written graphing code. The approximation for tet was obtained from the article on the tetration at the Citizendium and from Kouznetsov's papers, both of which list coefficients. The papers also describe the methods for obtaining them. I don't have the money to get programs like Mathematica, which costs like 1 to 2 thousand bucks or something.
And that's interesting about the ringing, it confirms the lack of a viable asymptotic here even without looking at the complex graph.
So it would seem that the "cheta" method is not a good method for extending tetration.
