Wigner 3-j symbols.

v = wigner3j(j1,j2,j3,m1,m2,m3)
v = wigner3j(jm1,jm2,jm3)
v = wigner3j(jjj,mmm)
v = wigner3j(jjjmmm)

wigner3j returns the value of the 3-j symbol

The six parameters can be specified separately or in groups. In the three-argument form, wigner3j takes jm1 = [j1 m1], jm2 = [j2 m2] and jm3 = [j3 m3]. If two arguments are given, it takes jjj = [j1 j2 j3] and mmm = [m1 m2 m3]. If one argument is give, it takes the 2x3 array jjjmmm = [j1 j2 j3; m1 m2 m3].

wigner3j returns accurate values for j values as large as several thousand.

wigner3j([1 1 0; 0 0 0])

ans =
   -0.57735

wigner3j([4 2 4; -2 -1 3])

ans =
    0.19462

If any of the three j values is less or equal to 2, wigner3j uses explicit expressions. For larger values, a general expression containing an alternating sum of binomial coefficients is used. For j values large than about 20, high-precisions arithmetic is used internally.

wigner3j implements expressions from

• E. R. Edmonds, Angular Momentum, Princeton University Press, 1957
• Shan-Tao Lai, Ying-Nan Chiu, Computer Physics Communications 61, 350-360 (1990)
• Liqiang Wei, Computer Physics Communications 120, 222-230 (1999)
• Robert E. Tuzun, Paul Burkhardt, Don Secrest, Computer Physics Communications 112, 112-148 (1998)

clebschgordan, wigner6j, wignerd