\[\nabla^{2}f=\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{%
\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+\frac{1}{r}\frac{%
\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}{{\partial\phi}^{%
2}}.\]