About: We can of course regard a function f defined on \mathbb{R}^{2n} as a function defined on \mathbb{C}^{n}. If f is differentiable on \mathbb{R}^{2n}, it is said to be real-differentiable, and if f is differentiable on \mathbb{C}^{n}, it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.     Permalink

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