Improving convergence of Andrew's slog

[quickfur]

Wow! Just out of curiosity, Jay, have you made any progress on this front? This is quite fascinating. I read Andrew's paper, and while there are still open issues, the idea of an extension of tetration to real numbers that is both \( C^{\infty} \) and satisfies \( x[4]y = x^{x[4](y-1)} \) for all real y really appeals to me. I think the basic approach is in the right direction: in general, functions induced by the hyper operators have extreme growth rates, and something about this fact causes analysis to be very difficult. But their inverse functions have sane rates of growth (that is to say, extremely slow), and should be much easier to study.