You have the CR equations in polar and cartesian coördinates that are equivalent if f(z) is complex differentiable because you can use the chain rule on u and v but if f isn't differentiable you can find an easy example where only the x-y CR hold but the polar partials don't even exist. My question now is is there a less strict requirement (than complex differentiable) under which the CR are equivalent?
2026-03-26 08:14:53.1774512893
Equivalence of Cauchy-Riemann equations
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