Racah coefficient

The Racah V-coefficients are written V(j_1 j_2 j;m_1 m_2 m) and are sometimes expressed using the related Clebsch-Gordan coefficients C_(m_1 m_2)^j = (j_1 j_2 m_1 m_2|j_1 j_2 j m), or Wigner 3j-symbols. Connections among the three are (j_1 j_2 m_1 m_2|j_1 j_2 m) = (-1)^(-j_1 + j_2 - m) sqrt(2j + 1)(j_1 | j_2 | j m_1 | m_2 | -m) (j_1 j_2 m_1 m_2|j_1 j_2 j m) = (-1)^(j + m) sqrt(2j + 1)V(j_1 j_2 j;m_1 m_2 - m) V(j_1 j_2 j;m_1 m_2 m) = (-1)^(-j_1 + j_2 + j)(j_1 | j_2 | j_1 m_2 | m_1 | m_2).

Clebsch-Gordan coefficient | Racah W-coefficient | Wigner 3j-symbol | Wigner 6j-symbol | Wigner 9j-symbol