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An Introduction to Complex Differentials and Complex ...

The next theorem provides conditions under which the Cauchy-Riemann equations are sufficient for f(z) being holomorphic. Theorem 2.0.2: If the partial derivatives of U(x;y) and V(x;y) with respect to xand yare con-tinuous, the Cauchy-Riemann equations are sufficient for f(z) being holomorphic. Proof: See [Spiegel, 1974]. 2

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