I need to apply a function $f(x)$ recursively/repeatedly for n times; how do I express it (mathematically) ? Is their a mathematical symbol which denotes $f(x)$ applied n times ie $g(x,n)$ =$f(f(\dots_{ times \quad n}(x)))\dots)$ ** With a variable parameter ** $h[x,1,n)]$ =$f(1,f(2,\dots_...

If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use? For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is important especially since I am trying to couple this with a limit toward infinity.

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

Is there a simpler expression for $f(f(f(...f(x)...)))$ (total n '$f$') ? Thank you.