>>12611533This fact is pretty obvious.
When we have a function restricted by the differential equation , it will clearly be analytic because the equation bounds the roughness growth of the recursive derivative.
When a function is complex differentiable, all that means is the real and complex components are each multivariate differentiable, AND those components are restricted by the Cauchy-Riemann differential equation. This differential equation slows the roughness of the recursive derivatives (preventing infinite slopes, among more general improvements), guaranteeing analyticity.
