Since the integral equals the complex conjugate of the interior multipole moments I 2 ℓ ℓ m of the second (peripheral) charge distribution, the energy formula reduces to the simple form U = 1 4 π π ε ε ∑ ∑ ℓ ℓ = 0 ∞ ∞ ∑ ∑ m = − − ℓ ℓ ℓ ℓ Q 1 ℓ ℓ m I 2 ℓ ℓ m ∗ ∗