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I posted this question, quite a while ago, on math.stackexchange.com, here. I received an interesting answer but not sufficiently accurate for my purposes, so I'm trying here. I have a class of ...

Let $I\subseteq \mathbb{R}$ an open interval. Let $f:I\rightarrow \mathbb{C}$ real analytic. Suppose we want to numerically compute an analytic extension of $f$. We will assume the following: we are ...