In the case where integers are involved, the coefficients can be related to integrals of spherical harmonics : ∫ ∫ 4 π π Y ℓ ℓ 1 m 1 ∗ ∗ ( Ω Ω ) Y ℓ ℓ 2 m 2 ∗ ∗ ( Ω Ω ) Y L M ( Ω Ω ) d Ω Ω = ( 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 ⟩ ⟩