Category:Definitions/Harmonic Polynomials

This category contains definitions related to Harmonic Polynomials.
Related results can be found in Category:Harmonic Polynomials.

Let $\map P z$ be a polynomial over the complex numbers.

Then $\map P z$ is a harmonic polynomial if and only if its Laplacian is $0$.

That is, if and only if it satisfies Laplace's equation:

$\nabla^2 \map P z = 0$

That is, if and only if $\map P z$ is a harmonic function.