Complex Analysis: The Argument Principle in Analysis and Topology |
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Complex Analysis: The Argument Principle in Analysis and Topology Alan F. Beardon Limited preview - 2019 |
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a₁ absolutely convergent an(z analytic functions Argument Principle assume branch of Arg C(zo Cauchy's Theorem choice of Arg circle closed curve compact subset complex numbers component contains continuous choice continuous function cycle D₁ deduce defined definition denote disc of convergence domain E₁ Example Exercise exists a branch EZ₁ f be analytic finite number function f ƒ is continuous ƒ is differentiable g is analytic geometric given hence homeomorphic inequality inside integer Jordan curve Let f let ƒ loge maps Möbius transformation n₁ non-empty non-zero nth root number of zeros open set polygonal curve polynomial positive integer positive number power series proof of Theorem Prove r₂ rational function reader real numbers result satisfying sequence shows simply connected sin² sinh suppose uniform convergence w₁ w₂ y₁ z₁ z₂