11/10/2013, 11:10 PM
(11/09/2013, 07:36 AM)mike3 Wrote: .... The case \( e^{-e} \) is really interesting since it lies on the Shell-Thron border and has pseudo-period 2 at the principal fixed point, and as far as I can tell, there's hasn't yet been a good construction of the merged/bipolar superfunction (i.e. the tetrational, \( \mathrm{tet} \)) at this base. sheldonison mentioned some work toward this, though. Nonetheless, with the HAM, it looks to be possible to construct what would be that superfunction, and perhaps this might point the way towards tetrating it with sheldonison's merge method, or just providing a new, independent method, though it seems choosing the right initial guess is one of the tricky aspects here. I have managed, however, to successfully tetrate base \( -1 \).I'm also interested in any results for \( \exp^{-e} \), with pseudo period 2, as per our earlier discussion on this forum. I haven't gotten any further with that base, though I believe it has a solution possible due to results I've gotten for a base with pseudo period=5, via a cumbersome indirect method.
- Sheldon
- Sheldon