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

Thank you.

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    It seems that this question was asked several times on this site: [here](http://math.stackexchange.com/questions/8$1$$1$1/a-short-way-to-say-ffffx), [here](http://math.stackexchange.com/questions/247710/notation-for-repeated-application-of-function) and [here](http://math.stackexchange.com/questions/453575/recursive-application-of-a-function-symbol-of).2013-10-03

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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.

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    Yeah, $f^{(n)}$ is sometimes used for the $n-th$ derivative.2012-10-24