If f=u+iv and u and v satify the Cauchy-Riemann equations does that imply that f is analytic? or do we need more conditions

Question

If f=u+iv and u and v satisfy the Cauchy-Riemann equations does that imply that f is analytic? or do we need more conditions

Answer 1

If $u$ and $v$ are real differentiable functions, then holomorphicity of $f$ is equivalent to satisfaction of the Cauchy-Riemann equations.

But $f$ is holomorphic if and only if analytic.

Here's a discussion.