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fundamental theorems in complex analysis
The following is a list of fundamental theorems in the subject of complex analysis (single complex variable). If a theorem does not yet appear in the encyclopedia, please consider adding it — Planet Math is a work in progress and even some basic results have not yet been entered. Likewise, if some basic theorem has been overlooked in this list, please add it.

Cauchy’s integral theorem

Morera’s theorem

Cauchy’s integral formula

Cauchy’s residue theorem

Cauchy’s argument principle

Rouché’s theorem

Riemann’s removable singularity theorem

CasoratiWeierstrass theorem

implicit function theorem for complex analytic functions (I gave proofs of this and the next theorem in a posting to a forum and must convert them to an encyclopaedia entry.)

inverse function theorem for complex analytic functions

Liouville’s theorem

Weierstrass’ factorization theorem

Weierstrass’ criterion of uniform convergence

MittagLeffler’s theorem

MÃ¶bius circle transformation theorem

Schwarz’ reflection principle

Harnack’s principle

Runge’s theorem

Mergelyan’s theorem

Montel’s theorem

Marty’s theorem

Hurwitz’s theorem

Bieberbach’s conjecture

Koebe onefourth theorem
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