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I was thinking of the following problem. Let $f$ be a Taylor expansion and $a_k$ the associated coefficients, $$\forall x\in\mathbb{R},~f(x)\triangleq\sum_{k=0}^\infty a_kx^k.$$ Let suppose that we ...

My goal is to prove (or disprove) that sufficiently smooth and quickly decaying cutoff functions being tacked on to a Taylor series correctly extend the radius of convergence to the analytic ...