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Rouché's theorem (Theorem)

Let $ f,g$ be analytic on and inside a simple closed curve $ C$. Suppose $ \vert f(z)\vert>\vert g(z)\vert$ on $ C$. Then $ f$ and $ f+g$ have the same number of zeros inside $ C$.



"Rouché's theorem" is owned by Johan.
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proof of Rouché's theorem (Proof) by rspuzio
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Cross-references: number, simple closed curve, analytic
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This is version 5 of Rouché's theorem, born on 2003-04-28, modified 2004-04-14.
Object id is 4218, canonical name is RouchesTheorem.
Accessed 3321 times total.

Classification:
AMS MSC: 30E20 (Functions of a complex variable :: Miscellaneous topics of analysis in the complex domain :: Integration, integrals of Cauchy type, integral representations of analytic functions)
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