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Date: 24-5-2018
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Date: 20-12-2018
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Date: 22-5-2018
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The harmonic conjugate to a given function is a function such that
is complex differentiable (i.e., satisfies the Cauchy-Riemann equations). It is given by
where , , and is a constant of integration.
Note that is a closed form since is harmonic, . The line integral is well-defined on a simply connected domain because it is closed. However, on a domain which is not simply connected (such as the punctured disk), the harmonic conjugate may not exist.
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