Axial multipole moments are a series expansion of the electric potential of a charge distribution localized close to the origin along one Cartesian axis, denoted here as the z -axis. However, the axial multipole expansion can also be applied to any potential or field that varies inversely with the distance to the source, i.e., as 1 R . For clarity, we first illustrate the expansion for a single point charge, then generalize to an arbitrary charge density λ λ ( z ) localized to the z -axis.