# Multiple composition of function notation

Let's say I have a set of $n$ functions of $m$ variables: $$f_1(x_1,x_2,\ldots,x_m),f_2(x_1,x_2,\ldots,x_m),\ldots,f_n(x_1,x_2,\ldots,x_m)$$

Is there a notation that represents $(f_1 \circ f_2 \circ \cdots \circ f_n)(x_1,x_2,\ldots,x_m)$?

Basically, is there an equivalent of $\sum$, $\prod$, $\bigcup$, etc. for function composition? I have looked at several other threads on this site regarding this, but I have not found one containing a definite answer that satisfies me.

• do the $f_i$'s also have $m$ components? otherwise the composition isn't well-defined. As for the proper question, there is no common symbol for $n$ times composition. – user251257 Sep 18 '15 at 1:47
• – IV_ Feb 24 '18 at 21:06