I know that analytic implies infinitely differentiable, but is the converse always true as well?
2026-03-27 17:50:23.1774633823
Does infinitely differentiable imply analytic?
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Our old friend $$f(x) = e^{-\frac{1}{x^2}}$$ is infinitely differentiable and in particular at $x=0$ all its derivatives are zero. But it is not analytic at $x=0$.