Faber polynomials

In mathematics, the Faber polynomials P_m of a Laurent series

${\displaystyle \displaystyle f(z)=z^{-1}+a_{0}+a_{1}z+\cdots }$

are the polynomials such that

${\displaystyle \displaystyle P_{m}(f)-z^{-m}}$

vanishes at z=0. They were introduced by Faber (1903, 1919) and studied by Grunsky (1939) and Schur (1945).