(Deformation principle) If the integral of a function fez) over the unit circle equals 3

Chapter 14, Problem 14.1.51

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(Deformation principle) If the integral of a function f(z) over the unit circle equals 3 and over the circle |z| = 2 equals 5, can we conclude that f(z) is analytic everywhere in the annulus 1 < |z| < 2?

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