What is "harmonic function"

n. (context mathematics English) A function of two, three or n variables which is a solution to any of Laplace's equations

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of R) which satisfies Laplace's equation, i.e.

$$\frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0$$

everywhere on U. This is usually written as

∇f = 0

or

$$\textstyle \Delta f = 0$$