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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Is there a function $f$ that is a finite sum of functions with finite products of the inputs...

Note: This question aims to be a generalization of Is it possible to create a polynomial $p(x)$ with this relation between $p(0)$ and $p(c)$? and Is it possible to create a polynomial $p(x)$ with this …
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