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Harmonic functions

Any function which satisfies the Laplace's equation is known as a harmonic function.
If f(z) = u + iv is an analytic function, then u and v are both harmonic functions.

2u/∂x2 + ∂2u/∂y2 = 0
2v/∂x2 + ∂2v/∂y2 = 0

Such functions u,v are called Conjugate harmonic functions as u + iv is also analytic function.