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    Wigner 6j-symbol

    Result

    1/(5 sqrt(21))≈0.0436436

    Alternate form

    sqrt(21)/105

    Alternative representation

    { 1 | 2 | 3 2 | 1 | 2 } = ( sum_(m_1=-1)^1 sum_(m^^_1=-1)^1 sum_(m_2=-2)^2 sum_(m^^_2=-2)^2 sum_(m_3=-3)^3 sum_(m^^_3=-3)^3 sum_(m_4=-2)^2 sum_(m^^_4=-2)^2 sum_(m_5=-1)^1 sum_(m^^_5=-1)^1 sum_(m_6=-2)^2 sum_(m^^_6=-2)^2 δ_(m_1, -m^^_1) δ_(m_2, -m^^_2) δ_(m_3, -m^^_3) δ_(m_4, -m^^_4) δ_(m_5, -m^^_5) δ_(m_6, -m^^_6) (-1)^(11 + m_1 + m_2 + m_3 + m_4 + m_5 + m_6) ( 1 | 2 | 3 m_1 | m_2 | m_3 ) ( 1 | 1 | 2 m^^_1 | m_2 | m^^_6 ) ( 2 | 1 | 3 m^^_4 | m^^_5 | m^^_3 ) ( 2 | 2 | 2 m^^_4 | m^^_2 | m_6 ) = sum_(m_1=-1)^1 sum_(m^^_1=-1)^1 sum_(m_2=-2)^2 sum_(m^^_2=-2)^2 sum_(m_3=-3)^3 sum_(m^^_3=-3)^3 sum_(m_4=-2)^2 sum_(m^^_4=-2)^2 sum_(m_5=-1)^1 sum_(m^^_5=-1)^1 sum_(m_6=-2)^2 sum_(m^^_6=-2)^2 (-1)^(11 + m_1 + m_2 + m_3 + m_4 + m_5 + m_6) δ_(m_1, -m^^_1) δ_(m_2, -m^^_2) δ_(m_3, -m^^_3) δ_(m_4, -m^^_4) δ_(m_5, -m^^_5) δ_(m_6, -m^^_6) ( 1 | 2 | 3 m_1 | m_2 | m_3 ) ( 1 | 1 | 2 m^^_1 | m_2 | m^^_6 ) ( 2 | 1 | 3 m^^_4 | m^^_5 | m^^_3 ) ( 2 | 2 | 2 m^^_4 | m^^_2 | m_6 ))

    Series representation

    { 1 | 2 | 3 2 | 1 | 2 } = (sqrt(0!) sqrt(7!) sum_(k=0)^2 ((-1)^k (6 - k)! (9 - k)!)/((2 - k)! ((7 - k)!)^2 k!))/(sqrt(2!) sqrt(5!))

    { 1 | 2 | 3 2 | 1 | 2 } = (sqrt(2!) sqrt(5!) sum_(k=0)^0 ((-1)^k (4 - k)! (2 + k)!)/((2 - k)! (-k)! k! (5 + k)!))/(sqrt(0!) sqrt(7!))

    { 1 | 2 | 3 2 | 1 | 2 } = (sqrt(2!)^3 sqrt(7!) sum_(k=0)^2 ((-1)^k (2 + k)! (4 + k)!)/((2 - k)! (k!)^2 (5 + k)!))/(sqrt(0!) sqrt(4!)^2 sqrt(5!))