Theory of Functions of a Complex Variable, Parte 11

according analytic analytic function angle approaches arbitrary belong boundary bounded called carrying choose circle closed coincides compact complex number condition connected consider consisting contains continuous corresponding defined definition denote derivative differentiable direction disk distinct domain G equal equation Example exists fact Figure find finite first follows formula function function f(z given hence imaginary implies inequality infinite integral interior interval inverse joining Jordan curve least length limit point mapping mean Moreover multiple neighborhood obtain Obviously origin passing plane point 20 pole positive Problem Proof Prove radius of convergence rational real axis rectifiable Remark represented respect result root satisfying segment sequence side straight line suppose takes Theorem unit variable write z-plane zero