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For numbers $x_1, \ldots, x_n$ one may write $$ \sum_{i = 1}^n x_i $$ for what might otherwise informally be written $x_1 + \cdots + x_n$.

For functions $f_1, \ldots, f_n$ is there similar notation for what might otherwise informally be written as $f_1 \circ \cdots \circ f_n$?

Ѕᴀᴀᴅ
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Mees de Vries
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    I've never seen any, but you do sometimes see composition written as concatenation (e.g. working with linear transformations), in which case a good old-fashioned $\prod$ could arguably work. You'd have to make sure there was no call for pointwise multiplication. – Theo Bendit Oct 11 '18 at 11:09

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Hint: The paper Notation for Iteration of Functions, Iteral by Valerii Salov from 2012 gives a survey of used notation of iterated functions. He also proposes a new notation, a so-called Iteral-operator to describe iteration of functions.

Markus Scheuer
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