Faber polynomials

Faber polynomials are a sequence of orthogonal polynomials that arise in the context of complex analysis and approximation theory. They are particularly associated with the problem of approximating analytic functions on the unit disk in the complex plane. For a given analytic function \( f \) defined on the unit disk, the Faber polynomial \( P_n(z) \) can be used to construct an approximation of \( f \) through a series representation.