The sigma notation for a sum is a symbol representing the addition of a series of numbers (and functions and a lot of other things) with an upper and lower bound.
It is similar with the uppercase pi notation representing multiplication.
I have not been able to find one for the composition of a series of functions. For example, I could notate $f_1\circ f_2\circ ...\circ f_n(x)$ as something like this:
$$\DeclareMathOperator*{\foo}{\text{$\Large \bigcirc$}}\left(\foo\limits^n_{i=1}f_i\right)(x)$$
I know that this is probably not a correct or standard way to notate it. That is why I am asking how it should be notated.