(11/10/2015, 09:38 AM)tommy1729 Wrote: Conjecture 3.1 fails because the left hand side has radius going to 0.Hmm, I've not yet settled everything about this in my mind. I've of course seen, that with increasing n the convergence-radius of the function decreases. However, as usually, if a function can be analytically continued (beyond its radius of convergence) for instance by Euler-summation, I assume, that the result is still meaningful. And we have here the possibility for Euler-summation, so I think there is a true analytic continuation. However, I don't know yet whether this can be correctly inserted in my conjecture-formula for the limit-case.

Quote:It is a mystery how you intend to solve the cases x^^(3/2) = v though.As I understand this, this is using fractional iteration heights. As I described my exercises, I'm concerned with the unknown bases, and am using integer heights so far, not fractional heights ( superroot, not superlog)

Gottfried

Gottfried Helms, Kassel