Introduction to Complex Analysis

a₁ analytic continuation analytic function arbitrary point assume b₁ boundary point bounded branch points Cauchy's integral formula circle complex numbers conformal mapping constant continued analytically converges uniformly corresponding defined denote derivative differentiable domain G doubly periodic function entire function equation Exercise exists expansion exponential function finite number formula G₁ G₂ half-plane harmonic function Hence homotopic infinite integral Jordan curve K₁ Let w(z linear transformation maximum principle neighborhood obtain period parallelogram plane point of G polygonal polynomial positive real axis power series primitive function primitive periods proof r₁ rational function Riemann mapping theorem Riemann surface right-hand side schlicht Section segment sequence simply connected simply connected domain single-valued slit subdomain tends to zero triangle unit disk vanishes w(zo w₁ w₁(z w₂ w₂(z y₁ z-plane z₂