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The Concept of an Analytic Function
General Properties of Rational Functions
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analytic continuation analytic function angle arbitrary point assume boundary point bounded branch points Cauchy's Cauchy's integral formula complex numbers conformal mapping constant converges absolutely converges uniformly corresponds defined denote derivative differentiable domain G doubly periodic function entire function equation Exercise exists expansion exponential function finite number formula function w(z half-plane harmonic function Hence infinite infinity integral inverse function Jordan curve Let w(z limiting points linear transformation maximum principle neighborhood obtain origin period parallelogram period-strip plane point of G point z0 polygon polynomial positive real axis power series primitive function primitive periods proof prove the following rational function real and imaginary Riemann sphere Riemann surface right-hand side satisfies schlicht Section segment sequence sheet simple poles simply connected simply connected domain single-valued slit subdomain surface Rw tends to zero triangle unit disk vanishes vector z-plane