More generally, in arbitrary curvilinear coordinates (ξ), ∇ ∇ 2 f = ∂ ∂ ∂ ∂ ξ ξ j ( ∂ ∂ f ∂ ∂ ξ ξ k g k j ) + ∂ ∂ f ∂ ∂ ξ ξ j g j m Γ Γ m n n = 0 , or ∇ ∇ 2 f = 1 | g | ∂ ∂ ∂ ∂ ξ ξ i ( | g | g i j ∂ ∂ f ∂ ∂ ξ ξ j ) = 0 , ( g = det { g i j } ) where g ij is the Euclidean metric tensor relative to the new coordinates and Γ denotes its Christoffel symbols.