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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 $[a, b]$ ...

A Lipschitz continuous function $f : [-1,1] \to \mathbb{C}$ has a unique representation as a series in terms of the Chebyshev polynomials $T_k$, $$ f(x) = \sum_{k = 0}^\infty a_k \, T_k(x) \qquad \...