If $f\in\mathcal{C}^\infty((0,1),\mathbb{R})$ verifies the following: \begin{equation} \forall x\in(0,1),\,\exists n\in\mathbb{N},\quad f^{(n)}(x)=0 \end{equation} Can $f$ be anything but a polynomial function?
2026-04-06 00:44:29.1775436269
Can this function be anything but a polynomial function?
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