The Laplacian operator in cylindrical coordinates is
∇ c y l 2 = 1 r ∂ ∂ r ( r ∂ ∂ r ) + 1 r 2 ∂ 2 ∂ θ 2 + ∂ 2 ∂ z 2 {\displaystyle \nabla _{cyl}^{2}={\frac {1}{r}}{\frac {\partial }{\partial r}}\left(r{\frac {\partial }{\partial r}}\right)+{\frac {1}{r^{2}}}{\frac {\partial ^{2}}{\partial \theta ^{2}}}+{\frac {\partial ^{2}}{\partial z^{2}}}}
