Disclaimer: I do not know that much math, so there might be obvious mistakes that I make in this question.
As far as I can tell, taking the derivative of $x^{x^x}$ infinitely is possible. However, this does not mean a Taylor series is possible. So what I am asking is, is it possible. I see 5 possible outcomes:
- It is possible, and the answer is known/easy enough to figure out
- It has been proven to be possible, but we don’t know what it is yet
- It has been proven to be impossible, and cannot be done
- It may or not be possible, we don’t know yet
- Other
So, which one of these is it?