08/22/2007, 11:28 PM
Well, I've prepared some graphs in the hope that I can address the question about my super-logarithm extension. The question was "are you sure?" about my super-logarithm definition not working for bases between 
. My only answer is to look at the graphs.
These are some graphs of the first three coefficients of the super-logarithm, i.e. the Abel function of
. In each graph there are multiple curves, each curve corresponds to a specific approximation; the approximations shown are roughly 
and the independant axis represents the base 
. What follows are graphs of 
as functions of b for 
for the functional equation  = A(x) +1)
with  = -1)
.
As you can see, when the base is between, although the matrix equation has a solution, the solutions (coefficients) do not seem to converge. This is what leads me to beleive that my super-logarithm definition will only work for 
.
Andrew Robbins
These are some graphs of the first three coefficients of the super-logarithm, i.e. the Abel function of
As you can see, when the base is between
Andrew Robbins