08/17/2007, 11:20 PM

If by my solution you mean through parabolic iteration of and by Daniel's you mean through hyperbolic iteration of , then yes, I'd be happy to provide some high-quality graphics and numerical tables. I still need to re-read Jay's solution, since it seems dependent on the super-logarithmic constant which I don't understand yet. Also you brought up an interesting point that may prevent comparison of all methods, since some methods work over non-overlapping intervals.

Tetration can be divided into several intervals in terms of what values of x in are valid for that definition: the parabolic point , the hyperbolic interval , and I suppose would you could call the elliptic? interval , which is what my definition of the super-logarithm is valid for. These are all closely tied to the interval of convergence of the infinite hyper-power which was found almost 230 years ago. My how time has passed...

Andrew Robbins

Tetration can be divided into several intervals in terms of what values of x in are valid for that definition: the parabolic point , the hyperbolic interval , and I suppose would you could call the elliptic? interval , which is what my definition of the super-logarithm is valid for. These are all closely tied to the interval of convergence of the infinite hyper-power which was found almost 230 years ago. My how time has passed...

Andrew Robbins