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Cauchy's integral theorem  |  Cauchy's theorem   (English)

Definition Niveau 4

Cauchy's theorem for triangles: let D be a domain and f : D → C be holomorphic. Then if T is a triangle lying entirely in D ,



∂T 
f(z) dz=0,
where ∂T is the boundary of T . Compare Morera's theorem.
Cauchy's theorem for a star domain: let D be a star domain and f : D → C be holomorphic. Then



ϕ 
f(z) dz=0
for all closed paths ϕ in D .

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