Given some $f(x)$ composed with itself $n$ times, how would one go about finding a closed-form expression in terms of $x$ and $n?$
Specifically, I'm trying to find a function in two natural number variables, $f(x,y) = x^{(x^{(...^{(x^x)})^...)})} =$ "$x$ tetrated to the $y$".
Any resources for learning more about function composition at an undergraduate level would be very much appreciated
This doesn't have a closed form solution unfortunately.
Wikipedia has some good information on function iteration, and has a section on techniques to find closed forms.