Hi everyone: Suppose $f$ and $g$ are two real analytic functions on a bounded domain $D$ of $\mathbb{R}^{n}$ and we have
$$0\leq f(x)\leq g(x)$$ on $D$. Suppose the Taylor series associated to $g$ about $x_{0}$ is convergent for $|x-x_{0}|
Convergence of Talyor series of a real analytic function
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real-analysis
complex-analysis
1 Answers
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Hint: try $n=1$, $x_0 = 0$, $f(x) = 1/(1+x^2)$ and $g(x) = 1$.