(06/04/2011, 03:05 PM)sheldonison Wrote: Yeah, I think that's a big change in the function there. Do you have a reference on the "shell tron region"? I seem to remember reading about it many times, "Kidney bean shaped" region or something, but I don't know what the theory tells us happens.
For you I just created a first shot of the Shell-Thron region entry on the Hyperoperations Wiki
. (anyone may) feel free to improve and extend Quote:Also, Kneser mappings probably won't work from attracting fixed points, unless there are repeating regions of superexponential growth as real(x) grows. For example, the lower sexp superfunction of eta definitely lacks such superexponential growth, as real(x) grows. Also, the lower superfunction for sexp sqrt(2). Instead, both of those functions converge to the fixed point as real(x) grows, for all imag(z).
Oh this might indicate that the Kneser mapping is only possible for (and continuable to) bases outside the Shell-Thron region!