For clarity, we illustrate the expansion for a point charge, then generalize to an arbitrary charge density ρ ρ ( r ′ ) . Through this article, the primed coordinates such as r ′ refer to the position of charge(s), whereas the unprimed coordinates such as r refer to the point at which the potential is being observed. We also use spherical coordinates throughout, e.g., the vector r ′ has coordinates ( r ′ , θ θ ′ , ϕ ϕ ′ ) where r ′ is the radius, θ θ ′ is the colatitude and ϕ ϕ ′ is the azimuthal angle.