## Harmonic Function n variables

Hello, I need to give a harmonic function of n variables. It must satisfy:

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

It mentions that any function of class $C^2$ that satisfies it is called a harmonic function.

So, from what I can tell the function:

$f(x_1,x_2,...,x_n) = A_1x_1 + A_2x_2 + . . . + A_nx_n$

would satisfy the condition of finding a harmonic function of n variables. Also, I believe it is of class $C^2$, but I am not entirely sure. Thanks for verification!