sqrt(5/33)≈0.389249

sqrt(165)/33

〈5 4 0 0 | 5 4 1 0〉 = -sqrt(3) ( 5 | 4 | 1 0 | 0 | 0 )

〈5 4 0 0 | 5 4 1 0〉 = (sqrt(binomial(8, 8)) sqrt(binomial(10, 8)) sum_(k=4)^4 (-1)^k binomial(0, 4 - k) binomial(2, 5 - k) binomial(8, k))/(sqrt(binomial(2, 1)) sqrt(binomial(8, 4)) sqrt(binomial(10, 5)) sqrt(binomial(11, 8)))

〈5 4 0 0 | 5 4 1 0〉 = -(sqrt(3) sqrt(1!)^2 sqrt(8!) sum_(k=0)^1 ((-1)^k (5 + k)!)/((1 - k)! k! (3 + k)!))/(sqrt(0!) sqrt(2!) sqrt(11!))

〈5 4 0 0 | 5 4 1 0〉 = (sqrt(3) sqrt(0!) sqrt(8!) sqrt(11!) sum_(k=0)^0 ((-1)^k (2 - k)! (5 - k)!)/((1 - k)! (11 - k)! (-k)! k!))/(sqrt(2!) sqrt(4!)^2)

〈5 4 0 0 | 5 4 1 0〉 = (_3 F^~_2(-8, -5, -4;-2, -3;1) δ_(0, 0) sqrt(3) sqrt(0!) sqrt(1!)^2 sqrt(2!) sqrt(4!) sqrt(5!))/(sqrt(4!) sqrt(5!) sqrt(8!) sqrt(11!))

〈5 4 0 0 | 5 4 1 0〉 = (5! _3 F_2(0, 6, -1;2, -5;1) δ_(0, 0) (-1)^4 sqrt(3) sqrt(1!) sqrt(2!) sqrt(5!) sqrt(8!))/((1! sqrt(1!) sqrt(4!)^2 sqrt(5!)) (sqrt(0!) sqrt(11!)))

〈5 4 0 0 | 5 4 1 0〉 = (2! _3 F_2(0, 9, -1;-2, 5;1) δ_(0, 0) (-1)^4 sqrt(3) sqrt(4!) sqrt(5!)^2 sqrt(8!))/((4! sqrt(1!)^2 sqrt(4!)) (sqrt(0!) sqrt(2!) sqrt(11!)))