It follows from this and orthonormality of the spherical harmonics that CG coefficients are in fact the expansion coefficients of a product of two spherical harmonics in terms of a single spherical harmonic: Y ℓ ℓ 1 m 1 ( Ω Ω ) Y ℓ ℓ 2 m 2 ( Ω Ω ) = ∑ ∑ L , M ( 2 ℓ ℓ 1 + 1 ) ( 2 ℓ ℓ 2 + 1 ) 4 π π ( 2 L + 1 ) ⟨ ⟨ ℓ ℓ 1 0 ℓ ℓ 2 0 | L 0 ⟩ ⟩ ⟨ ⟨ ℓ ℓ 1 m 1 ℓ ℓ 2 m 2 | L M ⟩ ⟩ Y L M ( Ω Ω )