Given an analytic function $f(x)$ (say as combination of elementary functions and operators), is it possible to compute $n$ first bits of the value of the function on the whole interval $[a, b]$ inside the circle of convergence in polynomial time? For example, if the function is bounded on $\mathbb{R}$ and oscillating if we don't allow to use argument reduction? What if we restrict on the case of holonomic functions and use van der Hovens method?.
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$\begingroup$ Similar question: mathoverflow.net/questions/116536/easy-functions?rq=1 $\endgroup$– Alexandre EremenkoCommented Nov 27 at 13:25
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