The electric potential due to a point charge located at r ′ is given by Φ Φ ( r ) = q 4 π π ε ε 1 R = q 4 π π ε ε 1 r 2 + r ′ ′ 2 − − 2 r ′ r cos ⁡ ⁡ γ γ . where R = d e f | r − − r ′ | is the distance between the charge position and the observation point and γ γ is the angle between the vectors r and r ′ . If the radius r of the observation point is greater than the radius r ′ of the charge, we may factor out 1/ r and expand the square root in powers of ( r ′ / r ) < 1 using Legendre polynomials Φ Φ ( r ) = q 4 π π ε ε r ∑ ∑ ℓ ℓ = 0 ∞ ∞ ( r ′ r ) ℓ ℓ P ℓ ℓ ( cos ⁡ ⁡ γ γ ) This is exactly analogous to the axial multipole expansion.