Notes on Complex Function Theory |
Common terms and phrases
branch of log Cauchy-Riemann equations Cauchy's theorem closed curve complex function theory complex plane complex-valued function constant continuous function contour converges locally uniformly converges uniformly cosh counterclockwise orientation denote differentiable domain G equality example Exercise f(zo finitely follows formula function f function in G ƒ and g ƒ is holomorphic geometric half-plane harmonic function holomorphic function inequality inverse isolated singularity Laurent series Let f Let ƒ Let G linear fractional transformation log ƒ logarithm n-th root nonconstant obtain open disk open set open subset polynomial positive integer positive number power series preceding proof Prove R₁ radius of convergence rational functions real axis real numbers real-valued removable singularity Riemann mapping Section sequence simple simply connected simply connected domain subset G triangle unit circle vanishes winding number z₁ z1 and z2 zeros of ƒ Σπί ди მა მე მყ