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    Wigner 3j-symbol

    Result

    sqrt(5/143)≈0.186989

    Alternate form

    sqrt(715)/143

    Alternative representation

    ( 6 | 4 | 2 0 | 0 | 0 ) = (〈6 4 0 0 | 6 4 2 0〉)/sqrt(5)

    Series representations

    ( 6 | 4 | 2 0 | 0 | 0 ) = (sqrt(binomial(8, 8)) sqrt(binomial(12, 8)) sum_(k=4)^4 (-1)^k binomial(0, 4 - k) binomial(4, 6 - k) binomial(8, k))/(sqrt(5) sqrt(binomial(4, 2)) sqrt(binomial(8, 4)) sqrt(binomial(12, 6)) sqrt(binomial(13, 8)))

    ( 6 | 4 | 2 0 | 0 | 0 ) = (sqrt(2!)^2 sqrt(8!) sum_(k=0)^2 ((-1)^k (6 + k)!)/((2 - k)! k! (2 + k)!))/(sqrt(0!) sqrt(4!) sqrt(13!))

    ( 6 | 4 | 2 0 | 0 | 0 ) = (sqrt(0!) sqrt(8!) sqrt(13!) sum_(k=0)^0 ((-1)^k (4 - k)! (6 - k)!)/((2 - k)! (13 - k)! (-k)! k!))/sqrt(4!)^3

    Hypergeometric-type representations

    ( 6 | 4 | 2 0 | 0 | 0 ) = (_3 F^~_2(-8, -6, -4;-1, -3;1) δ_(0, 0) sqrt(0!) sqrt(2!)^2 sqrt(4!)^2 sqrt(6!))/(sqrt(4!) sqrt(6!) sqrt(8!) sqrt(13!))

    ( 6 | 4 | 2 0 | 0 | 0 ) = (6! _3 F_2(0, 7, -2;3, -6;1) δ_(0, 0) sqrt(2!) sqrt(4!) sqrt(6!) sqrt(8!))/((-1)^6 (2! sqrt(0!) sqrt(2!) sqrt(4!)^2 sqrt(6!) sqrt(13!)))

    ( 6 | 4 | 2 0 | 0 | 0 ) = (6! _3 F_2(7, -6, -2;-6, 3;1) δ_(0, 0) (-1)^4 sqrt(2!) sqrt(4!) sqrt(6!) sqrt(8!))/(2! sqrt(0!) sqrt(2!) sqrt(4!)^2 sqrt(6!) sqrt(13!))

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