On the symmetries of the Racah coefficient

Abstract

Observations on the symmetries of the Racah coefficient are made in terms of its three allowed series representations. The Bailey’s transform between the two terminating Saalschutzian ₄F₃(1) series, when applied to the ₄F₃(1) representation for the Racah coefficient, is shown to result (at best) in the allowed substitution j → −j −1 for any one of the six angular momenta in the Racah coefficient.