In spherical coordinates, using the ( r , θ θ , φ φ ) convention, ∇ ∇ 2 f = 1 r 2 ∂ ∂ ∂ ∂ r ( r 2 ∂ ∂ f ∂ ∂ r ) + 1 r 2 sin ⁡ ⁡ θ θ ∂ ∂ ∂ ∂ θ θ ( sin ⁡ ⁡ θ θ ∂ ∂ f ∂ ∂ θ θ ) + 1 r 2 sin 2 ⁡ ⁡ θ θ ∂ ∂ 2 f ∂ ∂ φ φ 2 = 0.