# Notation for Composition and product of a function

I am confused about notation for composition and products of a function $f$. I know that $f \circ f$ implies composition but how we will denote product of same function and whether there is another way to write $f \circ f$?

• write parentheses if unsure which goes first, $(f\circ f) g = f(f)\cdot g$, $f\circ (g\cdot f) = f(g\cdot f)$ – mathreadler Aug 29 '17 at 16:54

The product of $f$ with itself is $f.f$, $f\times f$, or $f^2$.
• This would be a better Answer if you gave the contrast between notation for the product of $f$ with itself versus the composition of $f$ with itself. – hardmath Aug 29 '17 at 17:12
• @alearner Yes: $f^{(2)}$. More generally, the composition of $f$ with itself $n$ times is denoted by $f^{(n)}$. – José Carlos Santos Aug 29 '17 at 17:17
• @alearner I am sorry. I made a mistake. You are right about $f^{(n)}$. The standard notation for $f$ composed with itself $n$ times is $f^n$. Of course, in a context in which $f$ can be multiplied with itself you will have to be careful. – José Carlos Santos Aug 29 '17 at 17:41