Elementary Theory of Analytic Functions of One Or Several Complex Variables

analytic functions automorphism b₁ branch of log centre chapter circle closed disc closed path coefficients compact subsets completes the proof complex manifold complex manifold structure complex number complex variable connected open set consider constant contained continuous function converges normally converges uniformly coordinate deduce Definition denotes derivative differentiable path equal equation exists finite number follows formal power series formal series function f half-plane harmonic function holo holomorphic function holomorphic mapping homeomorphism identically zero infinite inverse isomorphism lemma Let f maximum modulus principle mean value property meromorphic function necessary and sufficient neighbourhood normally convergent open disc oriented boundary point at infinity pole polynomial power series expansion primitive proposition proved radius of convergence real axis real number rectangle relation residue Riemann sphere Riemann surface right hand side satisfies sequence simple simply connected space sufficiently small tends topology transformation unique unit disc z₁