07/31/2009, 08:11 PM
Well, I've been off with projects (experimenting with random number generators, learning lots about primes, 2-adic numbers, galois fields, spectral tests, lattice reduction, lattice covering and packing, and the like).
But I've decided to turn my interests back to tetration and related subjects.
One particular subject that I stopped investigating was my "cheta" function, which is essentially a scaled version of the continuous iteration of \( \exp(x)-1 \). (I stopped work on it mainly because I was using it to find a general solution to tetration using a change of base formula, and I unfortunately found that the results don't match those of the "natural" solution.)
So I've started tinkering with it again, slowly remembering old insights and forming new ones. Before I invest too much time, I was wondering how much has been discussed on this subject in my 1-2 year absence. Can someone point me to anything new that I should read up on before I get too far along? Relevant subjects include not only base \( e^{1/e} \), a.k.a. eta, but also the problem of non-convergence for non-integer iterates of functions, etc.
But I've decided to turn my interests back to tetration and related subjects.
One particular subject that I stopped investigating was my "cheta" function, which is essentially a scaled version of the continuous iteration of \( \exp(x)-1 \). (I stopped work on it mainly because I was using it to find a general solution to tetration using a change of base formula, and I unfortunately found that the results don't match those of the "natural" solution.)
So I've started tinkering with it again, slowly remembering old insights and forming new ones. Before I invest too much time, I was wondering how much has been discussed on this subject in my 1-2 year absence. Can someone point me to anything new that I should read up on before I get too far along? Relevant subjects include not only base \( e^{1/e} \), a.k.a. eta, but also the problem of non-convergence for non-integer iterates of functions, etc.
~ Jay Daniel Fox