Harmonic Functions are Real Parts of Holomorphic Functions

We prove that every harmonic function is locally the real part of a holomorphic function. The local assumption can be dropped if we assume that the region is simply connected. We use the Wirtinger operators to factor the Laplace equation in order to show that a function is harmonic if and only if the z derivative of the function vanishes. This allows us to prove that harmonic functions are the sum of a holomorphic function and an anti-holomorphic function

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Видео Harmonic Functions are Real Parts of Holomorphic Functions канала Mike, the Mathematician