Complex Analysis |
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a₁ absolute value analytic continuation analytic function analytic isomorphism assume b₁ boundary bounded calculus Cauchy's theorem centered Chapter closed disc closed path coefficients compact set complex numbers contained continuous function converges absolutely converges uniformly curve defined derivative differentiable disc of radius entire function equal equation Example EXERCISES exists f be analytic Figure finite number function f harmonic function Hence holomorphic function integral interval inverse lemma Let f Let f(z Let ƒ maximum modulus principle meromorphic open disc open set poles polynomial positive integer power series expansion Proof proves the theorem quotient radius of convergence real axis real numbers rectangle residue Riemann mapping theorem say that ƒ segment sequence Show shown on Fig subset Suppose Theorem 1.2 unit circle unit disc upper half plane w₁ whence write z₁ Σπί