The Mittag-Leffler Theorem is a fundamental result in complex analysis that provides conditions under which a meromorphic function can be represented as a sum of simpler fractions, specifically as a sum of terms of the form $$\frac{a_n}{z - z_n}$$, where the $z_n$ are the poles of the function. This theorem is significant because it establishes a method to construct meromorphic functions with prescribed poles and residues, linking it to other important concepts like the Weierstrass factorization theorem, which deals with entire functions and their representations.
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