bo198214 Wrote:In this line I would be really interested in the difference of Andrew's slog with the regular Abel function at the lower fixed point.

The formula for the latter, derived from here, is:

, where is the lower fixed point of .

Can you make a comparison of with Andrew's computed by your super sophisticated algorithm and post a graph of the difference in the range say [-1,1.9] somewhere?!

I can take a stab at it during the next week or two. I haven't tried out Andrew's slog with other bases yet, mainly because I've been so focussed on the base e solution. I'm not sure what will happen with a base less than eta, since the dynamics are a little different, but it should be interesting nonetheless.

Given the very small discrepancy between the regular slogs at the smaller and larger real fixed points, I'd think precision at least as good (if not a few digits more) will be needed to answer this question.

~ Jay Daniel Fox