Let p be a positive integer. Consider the closed curve γ(t) = e it , 0 ≤ t 1. If f has a zero only at z 0 , 0 < |z 0 | < R, and it is of multiplicity q, then: 1 2πi ∫ γ f'(z) f(z) z p dz equals

Mathematics · Complex Analysis

Let p be a positive integer. Consider the closed curve γ(t) = e it , 0 ≤ t < 2π. Let f be a function holomorphic in {z : |z| < R} where R > 1. If f has a zero only at z 0 , 0 < |z 0 | < R, and it is of multiplicity q, then: 1 2πi ∫ γ f'(z) f(z) z p dz equals

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q z 0 p

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