Symmetries of some hypergeometric series: Implications for 3j- and 6j-coefficients

The occurrence of generalized hypergeometric series as factors, in the Wigner-Clebsch-Gordan (3j) and Racah (6j) coefficients is well known. The recently discovered S/sub 5/ symmetry of the Saalscheutzian /sub 4/F/sub 3/ series may be used to extend the symmetries of the 6j-coefficients to the much larger group generated by S/sub 5/ and the group of Regge symmetries. (A similar extension may be carried out for the 3j-coefficients). The required extension of the domain of definition of the 6j-coefficients and the properties of its symmetry group is developed here. 7 refs.