Wigner 3-j symbols.

v = wigner3j(j1,j2,j3,m1,m2,m3)
v = wigner3j(jm1,jm2,jm3)
v = wigner3j(j,m)

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] etc., if two arguments are given, it takes j = [j1 j2 j3] and m = [m1 m2 m3].

wigner3j returns accurate values as long as the maximum j is not larger than about 300.

wigner3j([1 1 0],[0 0 0])

ans =
   -0.5774

wigner3j([1 1 2],[0 0 0])

ans =
    0.3651

For small values of the input parameters, wigner3j uses specific expressions. For larger values, a general expression containing an alternating sum of binomial coefficients is used. If any of the j values is larger than 20, the Java BigInteger class is used to obtain accurate values.

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

clebschgordan, wigner6j