08/18/2007, 09:35 AM
I just wanted to clarify that my super-logarithm solution only works for 
even though my pdf says 
. I think that the reason for this is that tetration for bases between 1 and 
has an upper limit (due to the convergence of 
), and thus the super-logarithm has a limited domain over which it is defined. This upper limit of tetration also means that there will be a singularity on the boundary of this domain, which might explain why I have had such poor results as 
with experiments with my method.
When I first discovered the super-logarithm solution, the only singularities in the matrix equation (rather than the series expansion) seemed to be less than 1, this is what led me to the requirement, which I later learned to be not strict enough. Sorry. Hope this helps.
For an abstraction of my super-logarithm method, see http://math.eretrandre.org/tetrationforu...181#pid181
Andrew Robbins
When I first discovered the super-logarithm solution, the only singularities in the matrix equation (rather than the series expansion) seemed to be less than 1, this is what led me to the requirement
For an abstraction of my super-logarithm method, see http://math.eretrandre.org/tetrationforu...181#pid181
Andrew Robbins