jaydfox Wrote:You're not factoring in the superlogarithmic constant. You tetrate base b n+mu times, then take the logarithm base a only n times. If base b is greater than base a, then mu will be negative.

You gave the formula for arbitrary . So if is negative I simply choose such that for example (actually I tried and ). Otherwise you have to specify for which x your formula is valid (which makes it clear again that the convergence of your formula wasnt at all "obvious"). Normally the tetration shall be defined for exponents I guess.

However if we can show analyticity it suffices to define it in a small vicinity of some point because from there we can analytically extend it. However the question then is what is and what has the vicinity.