Runge’s theorem

Let $K$ be a compact subset of $ℂ$, and let $E$ be a subset of ${ℂ}_{\mathrm{\infty }}=ℂ\cup \{\mathrm{\infty }\}$ (the extended complex plane) which intersects every connected component of ${ℂ}_{\mathrm{\infty }}-K$. If $f$ is an analytic function in an open set containing $K$, given $\epsilon >0$, there is a rational function $R(z)$ whose only poles are in $E$, such that for all $z\in K$.

Title	Runge’s theorem
Canonical name	RungesTheorem
Date of creation	2013-03-22 13:15:12
Last modified on	2013-03-22 13:15:12
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Theorem
Classification	msc 30E10
Related topic	MergelyansTheorem