Let be compact, let be analytic on a neighborhood of , and let contain at least one point from each connected component of . Then for any , there is a rational function with poles in such that
(Krantz 1999, p. 143).
A polynomial version can be obtained by taking . Let be an analytic function which is regular in the interior of a Jordan curve and continuous in the closed domain bounded by . Then can be approximated with arbitrary accuracy by polynomials (Szegö 1975, p. 5; Krantz 1999, p. 144).