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

Question

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

Thank you.

It seems that this question was asked several times on this site: here, here and here. — Martin Sleziak, Oct 03 '13 at 14:48

score 7 · Accepted Answer · answered Oct 24 '12 at 12:51

7

The notation $f^n=\underset{\text{$n$-times}}{\underbrace{f\circ \dots \circ f}}$ is commonly used. (So $f(f(\dots f(x)\dots))=f^n(x)$.)

Occasionally this might be confused with $(f(x))^n$, i.e. the $n$-th power of the value $f(x)$, but it is usually clear from the context which of the two is meant.

See Wikipedia article Iterated function.

answered Oct 24 '12 at 12:51

Martin Sleziak

53,687

1

Usually to avoid confusion some people write $f^{(n)}(x)$, but then again this may be used somewhere else and just shifts the confusion. – Jean-Sébastien Oct 24 '12 at 12:59
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Yeah, $f^{(n)}$ is sometimes used for the $n-th$ derivative. – fgp Oct 24 '12 at 14:07

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

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