Question

cauhy reman equation

Answer 1

Suppose that f = u + iv is a complex-valued function which is differentiable as a function f : R2 → R2. Then Goursat's theorem asserts that f is analytic in an open complex domain Ω if and only if it satisfies the Cauchy–Riemann equation in the domain (Rudin 1966, Theorem 11.2).