The quantities in the symbol are called angular momenta. Either all of them are nonnegative integers, or one is a nonnegative integer and the other two are half-odd positive integers. They must form the sides of a triangle (possibly degenerate). They therefore satisfy the triangle conditions
where is any permutation of . The corresponding projective quantum numbers are given by
See Figure 34.2.1 for a schematic representation.
and the summation is over all nonnegative integers such that the arguments in the factorials are nonnegative.
where is defined as in §16.2.
For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§8.21, 8.24–8.26).