Suppose that $f(x)$ is an analytic complex or real function on the real domain and we only know $f(x_0)$ and the first $n$ derivatives of $f(x)$ at $x=x_0$. Is there an algorithm whose accuracy increases as $n$ gets larger that gives an approximation for the next derivative at the same point?
2026-03-25 16:01:29.1774454489
Extrapolating the sequence of derivatives of an analytic function
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