Mittag-Leffler’s theorem

Let G be an open subset of , let {ak} be a sequence of distinct points in G which has no limit pointMathworldPlanetmath in G. For each k, let A1k,,Amkk be arbitrary complex coefficients, and define


Then there exists a meromorphic function f on G whose poles are exactly the points {ak} and such that the singular part of f at ak is Sk(z), for each k.

Title Mittag-Leffler’s theorem
Canonical name MittagLefflersTheorem
Date of creation 2013-03-22 13:15:15
Last modified on 2013-03-22 13:15:15
Owner Koro (127)
Last modified by Koro (127)
Numerical id 4
Author Koro (127)
Entry type Theorem
Classification msc 30D30
Related topic WeierstrassFactorizationTheorem