It is straightforward to generalize these formulae by replacing the point charge q with an infinitesimal charge element ρ ρ ( r ′ ) d r ′ and integrating. The functional form of the expansion is the same. In the exterior case, where r > r ′ , the result is: Φ Φ ( r ) = 1 4 π π ε ε ∑ ∑ ℓ ℓ = 0 ∞ ∞ ∑ ∑ m = − − ℓ ℓ ℓ ℓ ( Q ℓ ℓ m r ℓ ℓ + 1 ) 4 π π 2 ℓ ℓ + 1 Y ℓ ℓ m ( θ θ , ϕ ϕ ) , where the general multipole moments are defined Q ℓ ℓ m = d e f ∫ ∫ d r ′ ρ ρ ( r ′ ) ( r ′ ) ℓ ℓ 4 π π 2 ℓ ℓ + 1 Y ℓ ℓ m ∗ ∗ ( θ θ ′ , ϕ ϕ ′ ) .