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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 $f \circ f$?

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  • $\begingroup$ write parentheses if unsure which goes first, $(f\circ f) g = f(f)\cdot g$, $f\circ (g\cdot f) = f(g\cdot f)$ $\endgroup$ – mathreadler Aug 29 '17 at 16:54
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The product of $f$ with itself is $f.f$, $f\times f$, or $f^2$.

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    $\begingroup$ 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. $\endgroup$ – hardmath Aug 29 '17 at 17:12
  • $\begingroup$ Okay sir thanks and is there any other notation for (fof) ? $\endgroup$ – a learner Aug 29 '17 at 17:12
  • $\begingroup$ @alearner Yes: $f^{(2)}$. More generally, the composition of $f$ with itself $n$ times is denoted by $f^{(n)}$. $\endgroup$ – José Carlos Santos Aug 29 '17 at 17:17
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    $\begingroup$ Okay sir but f^(n) can be used to denote n times differentiation of a function ,isn't it? $\endgroup$ – a learner Aug 29 '17 at 17:27
  • $\begingroup$ @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. $\endgroup$ – José Carlos Santos Aug 29 '17 at 17:41

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