Let us introduce the notation ρ ρ = k r . In the component form vector spherical harmonics are written as: M e m n ( k , r ) = − − m sin ⁡ ⁡ ( θ θ ) sin ⁡ ⁡ ( m φ φ ) P n m ( cos ⁡ ⁡ ( θ θ ) ) z n ( ρ ρ ) e θ θ − − cos ⁡ ⁡ ( m φ φ ) d P n m ( cos ⁡ ⁡ ( θ θ ) ) d θ θ z n ( ρ ρ ) e φ φ M o m n ( k , r ) = m sin ⁡ ⁡ ( θ θ ) cos ⁡ ⁡ ( m φ φ ) P n m ( cos ⁡ ⁡ ( θ θ ) ) z n ( ρ ρ ) e θ θ − − sin ⁡ ⁡ ( m φ φ ) d P n m ( cos ⁡ ⁡ ( θ θ ) ) d θ θ z n ( ρ ρ ) e φ φ