Runge’s theorem

Let K be a compact subset of , and let E be a subset of ={} (the extended complex plane) which intersects every connected componentMathworldPlanetmathPlanetmathPlanetmath of -K. If f is an analytic functionMathworldPlanetmath in an open set containing K, given ε>0, there is a rational function R(z) whose only poles are in E, such that |f(z)-R(z)|<ε for all zK.

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