Course Solutions Uncategorized (Solved) : 99 Use Residue Theorem 910 Re Prove Cauchy S Integral Formulas Theorems 427 51 Corollary 8 Q33346135 . . . .

(Solved) : 99 Use Residue Theorem 910 Re Prove Cauchy S Integral Formulas Theorems 427 51 Corollary 8 Q33346135 . . . .

 

9.9. Use the Residue Theorem 9.10 to re-prove Cauchys Integral Formulas (Theorems 4.27 & 5.1 and Corollary 8.11) Theorem 9.10 (Residue Theorem). Suppose f is holomorphic in the region G, except for isolated singu- larities, and γ is a positively oriented, simple, closed, pieceurse smooth path that avoids the singularities off, and γ ~G 0, Then there are only initely many singularities inside γ, and f-2πίΣ Res(f(z)) 2-2k where the sum is taken over all singularities zk inside γ Theorem 4.27 (Cauchys Integral Formula). Suppose f is holomorphic in the region G and γ is a positively oriented, simple, 

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