In this case, vector spherical harmonics are generated by scalar functions, which are solutions of scalar Helmholtz equation with the wavevector k . ψ ψ e m n = cos ⁡ ⁡ m φ φ P n m ( cos ⁡ ⁡ ϑ ϑ ) z n ( k r ) ψ ψ o m n = sin ⁡ ⁡ m φ φ P n m ( cos ⁡ ⁡ ϑ ϑ ) z n ( k r ) here P n m ( cos ⁡ ⁡ θ θ ) are the associated Legendre polynomials, and z n ( k r ) are any of the spherical Bessel functions.