Combining these results gives recursion relations for the Clebsch–Gordan coefficients, where C ± was defined in 1 : C ± ± ( J , M ) ⟨ ⟨ j 1 m 1 j 2 m 2 | J ( M ± ± 1 ) ⟩ ⟩ = C ± ± ( j 1 , m 1 ∓ ∓ 1 ) ⟨ ⟨ j 1 ( m 1 ∓ ∓ 1 ) j 2 m 2 | J M ⟩ ⟩ + C ± ± ( j 2 , m 2 ∓ ∓ 1 ) ⟨ ⟨ j 1 m 1 j 2 ( m 2 ∓ ∓ 1 ) | J M ⟩ ⟩ .