For studying tetration in general, I think the best place to start is with base eta, which can be solved using a continuous iteration of \( f(z)=e^z-1 \). Andrew has already posted functional SAGE code for this. I know I had to make a few additions to it, but it wasn't much, so let me know if you need help getting it to work with high precision (you should be able to get decently fast results with hundreds of digits of precision).
For a more complex (no pun intended) solution, consider the case of base e, which I'm confident will serve as a template for all bases greater then eta.
I'm nearly finished putting together a library for my accelerated version of Andrew's slog for base e. I think it'll be the most helpful solution for anyone wanting to study tetration as a newbie, especially complex tetration. Whether you're wanting to study complex tetration or real-valued tetration, Andrew's slog (and its inverse) seems to have several very wonderful properties that make it a strong contender for "the" solution, at least for base e.
I'm hoping to have the code ready to post within the next couple days. I'm automating steps I had been doing by hand, so hopefully this will be helpful for others as well.
For a more complex (no pun intended) solution, consider the case of base e, which I'm confident will serve as a template for all bases greater then eta.
I'm nearly finished putting together a library for my accelerated version of Andrew's slog for base e. I think it'll be the most helpful solution for anyone wanting to study tetration as a newbie, especially complex tetration. Whether you're wanting to study complex tetration or real-valued tetration, Andrew's slog (and its inverse) seems to have several very wonderful properties that make it a strong contender for "the" solution, at least for base e.
I'm hoping to have the code ready to post within the next couple days. I'm automating steps I had been doing by hand, so hopefully this will be helpful for others as well.
~ Jay Daniel Fox