Runge-Walsh Theorem

Let $f(x)$ be an Analytic Function which is Regular in the interior of a Jordan Curve $C$ and continuous in the closed Domain bounded by $C$. Then $f(x)$ can be approximated with arbitrary accuracy by Polynomials.

See also Analytic Function, Jordan Curve

References

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 7, 1975.