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).
