<P> In Cartesian coordinates, </P> <Dl> <Dd> Δ f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2 . (\ displaystyle \ Delta f = (\ frac (\ partial ^ (2) f) (\ partial x ^ (2))) + (\ frac (\ partial ^ (2) f) (\ partial y ^ (2))) + (\ frac (\ partial ^ (2) f) (\ partial z ^ (2))).) </Dd> </Dl> <Dd> Δ f = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2 . (\ displaystyle \ Delta f = (\ frac (\ partial ^ (2) f) (\ partial x ^ (2))) + (\ frac (\ partial ^ (2) f) (\ partial y ^ (2))) + (\ frac (\ partial ^ (2) f) (\ partial z ^ (2))).) </Dd> <P> In cylindrical coordinates, </P>

Laplacian of a scalar field in cylindrical coordinates