# Complex Chebyshev Polynomials

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?

• 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. – user147263 Sep 5 '15 at 3:07
• Thanks, that is definitely in the direction of what I am looking for. – Joel Turnblade Sep 6 '15 at 22:27