How can I find infinitely many functions $\displaystyle u:R^2 \rightarrow R$ that solve the Laplace equation? I think I need to find analytic functions $\displaystyle f$ in open subset $\displaystyle U \subset C$, but I don't know how to use the Cauchy Riemann equations here to help me. Someone can help please.

$\displaystyle \frac{\delta^2 u}{\delta x^2}+\frac{\delta^2 u}{\delta y^2}=0$