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Polyharmonic Functions 📂Functions

Polyharmonic Functions

Definition

Let $\Delta = \nabla^{2}$ be called a Laplacian. For a natural number $k \in \mathbb{N}$, $\Delta ^{k}$ is referred to as a polyharmonic operator or a polylaplacian. The equation below is called the polyharmonic equation.

$$ \Delta^{k} f = 0 $$

The solutions to the polyharmonic equation are referred to as polyharmonic functions.

Description

It is a generalization of harmonic functions.

See Also