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Given a function $f$, I want to refer to $f \circ f$ other than by a formula. Is there any name for this other than square of $f$, which has the problem of being ambiguous?

In analogy to the functional square root, using the functional square suggests itself but I fail to find any usage of this term that is related to mathematics but not not related to functional square roots.

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  • $\begingroup$ $f \circ f$ reads $f$ composed $f$ or composition of $f$ with itself, I don't know if there is a shorter name for it. $\endgroup$ – sciona Jan 15 '15 at 16:12
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Given that $f\circ f\circ\ldots\circ f\ $ ($n$ times) is called the $n$th iterate and the functional square root is often called half iterate, I'd call $f\circ f$ the second iterate of $f$.

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The closest you come in words is probably to speak about "$f$ iterated twice" or something like that.

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