Longitudinal harmonics: L o e m n ( k , r ) = ∂ ∂ ∂ ∂ r z n ( k r ) P n m ( cos ⁡ ⁡ θ θ ) sin cos m φ φ e r + 1 r z n ( k r ) ∂ ∂ ∂ ∂ θ θ P n m ( cos ⁡ ⁡ θ θ ) sin cos m φ φ e θ θ ∓ ∓ m r sin ⁡ ⁡ θ θ z n ( k r ) P n m ( cos ⁡ ⁡ θ θ ) cos sin m φ φ e φ φ