If the radius r of the observation point is greater than a, we may factor out 1 r and expand the square root in powers of ( a / r ) < 1 using Legendre polynomials Φ Φ ( r ) = q 4 π π ε ε r ∑ ∑ k = 0 ∞ ∞ ( a r ) k P k ( cos ⁡ ⁡ θ θ ) ≡ ≡ 1 4 π π ε ε ∑ ∑ k = 0 ∞ ∞ M k ( 1 r k + 1 ) P k ( cos ⁡ ⁡ θ θ ) where the axial multipole moments M k ≡ ≡ q a k contain everything specific to a given charge distribution; the other parts of the electric potential depend only on the coordinates of the observation point P. Special cases include the axial monopole moment M 0 = q , the axial dipole moment M 1 = q a and the axial quadrupole moment M 2 ≡ ≡ q a 2 . This illustrates the general theorem that the lowest non-zero multipole moment is independent of the origin of the coordinate system, but higher multipole moments are not (in general).