TITLE: A short way to say f(f(f(f(x))))
QUESTION [5 upvotes]: Is there a short way to say $f(f(f(f(x))))$?
I know you can use recursion:
$g(x,y)=\begin{cases}
f(g(x,y-1)) & \text{if } y > 0, \
\newline x & \text{if } y = 0.
\end{cases}$

REPLY [11 votes]: I personally prefer 
$f^{\circ n} = f \circ f^{\circ n-1} = \dotsb = \kern{-2em}\underbrace{f \circ \dotsb \circ f}_{n-1\text{ function compositions}}$