The Theory of Functions of a Complexe Variable: By R. Courant ; Notes Revised by A. A. BlankInstitute for Mathematics and Mechanics, New York University, 1948 - Functions of complex variables - 452 pages |
Common terms and phrases
accumulation point analytic continuation analytic function analytic function f(z angle arbitrarily boundary values bounded C₁ Cauchy Integral Cauchy-Riemann equations Cauchy's Integral Formula circle of convergence complex function complex numbers complex value connected domain consider constant continuous function converges uniformly corresponding cross ratio defined definition denote derivative differentiable entire function essential singularity finite number fixed points flow follows formula function element function-element functional equation geometry given harmonic function Hence infinite infinity interior inverse limit linear transformation mapping meromorphic function neighborhood obtain one-to-one origin P₂ plane point set polygon polynomial power series proof prove radius real and imaginary real functions real numbers regular function Riemann surface sequence series converges simple closed curve simple poles simply connected simply-connected domain single-valued subdivision sufficient suppose theorem unit circle upper half-plane vanishes z-plane z₁