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Chebyshev Polynomials can be used to compute a very nearly minimax polynomial approximation of an analytic function on $[-1,1]$. Is there a complex analog that can compute a nearly minimax polynomial for a holomorphic function on the unit disc?

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  • $\begingroup$ There is a natural and much-studied complex analog: the monic polynomial of smallest supremum on a given compact set. E.g., this paper and references there. For the unit disk this would be simply $z^n$. I don't know about using them to approximate a holomorphic function. $\endgroup$ – user147263 Sep 5 '15 at 3:07
  • $\begingroup$ Thanks, that is definitely in the direction of what I am looking for. $\endgroup$ – Joel Turnblade Sep 6 '15 at 22:27

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