In the following equations it is assumed that the triangle inequalities are satisfied and that is again defined by (34.3.4).
If any lower argument in a symbol is , , or , then the symbol has a simple algebraic form. Examples are provided by:
The symbol is invariant under interchange of any two columns and also under interchange of the upper and lower arguments in each of any two columns, for example,
In the following equation it is assumed that the triangle conditions are satisfied.
For generating functions for the symbol see Biedenharn and van Dam (1965, p. 255, eq. (4.18)).
Equations (34.5.15) and (34.5.16) are the sum rules. They constitute addition theorems for the symbol.
Equation (34.5.23) can be regarded as an alternative definition of the symbol.
For other sums see Ginocchio (1991).