The partial differential equation is known as Laplace’s equation, after Pierre...

The partial differential equation

is known as Laplace’s equation, after Pierre Simon de Laplace (1749–1827). Any function f of class C²

that satisfies Laplace’s equation is called a harmonic function.³

(b) We may generalize Laplace’s equation to functions of n variables as

Give an example of a harmonic function of n variables, and verify that your example is correct.