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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


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

© 1996-9 Eric W. Weisstein