The symbol is defined by the following double sum of products of symbols:
Except in degenerate cases the combination of the triangle inequalities for the four symbols in (34.4.1) is equivalent to the existence of a tetrahedron (possibly degenerate) with edges of lengths ; see Figure 34.4.1.
The symbol can be expressed as the finite sum
where 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, §§9.2.1, 9.2.3).