gives the values of the Wigner 3 symbol.


  • The 3 symbols vanish except when and the satisfy a triangle inequality.
  • The parameters of ThreeJSymbol can be integers, halfintegers or symbolic expressions.
  • The ClebschGordan coefficients and 3 symbols in the Wolfram Language satisfy the relation .


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Basic Examples  (2)

Use symbolic arguments to obtain exact symbolic answers:

Scope  (2)

ThreeJSymbol works with integer and halfinteger arguments:

TraditionalForm formatting:

Applications  (3)

Plot 3 symbol coefficients as a function of and :

Apply angular momentum operators to spherical harmonics:

Evaluate Gaunt coefficients:

Evaluate an explicit triple integral of spherical harmonics:

Properties & Relations  (4)

Evaluate the completely symbolic case of ThreeJSymbol:

Demonstrate sum orthogonality:

Convert to a Regge R symbol:

Check the symmetry of the Regge R symbol:

Compare with sum definition:

Possible Issues  (1)

A message is issued and the result 0 returned in the case :

Introduced in 1991