Journal of computational and applied mathematics vol:62 issue:2 pages:155-179
With any probability measure mu on [-1,1] we associate a sequence of polynomials F_n(z) which are Faber polynomials of a univalent function F(z) on |z| > 1. If the zeros of F_n(z) are in the open unit disk then there exists a Chebyshev-type quadrature formula for mu with n nodes which is exact for all polynomials f(t) up to degree n-1.
For the normalized Jacobi measures d mu(t) = C_lambda(1 - t)^(-1/2-lambda)(1 + t)^(-1/2) dt with lambda < 1/2 the function F(z) can be expressed in terms of hypergeometric functions. Using this expression it is proved that the zeros of the associated Faber polynomials are in the open unit disk in case lambda in (0,lambda_0] for some lambda_0 > 0. This result solves to a large extent a problem of Förster.