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Results tagged with power-series
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user 219013
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'Partial boundedness' of continuously parametrised power series
Take $D=[0,2]$, $a_i(x)=x^i$, then $f(x,1/3)$ converges for all $x\in D$, but $f(x,1)$ is unbounded as $x\to1$. So, unless I am misreading something in your question, the answer is negative.
EDIT: If …
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