ANGULAR AND HYPERANGULAR MOMENTUM COUPLING-COEFFICIENTS AS HAHN POLYNOMIALS

The relationship is investigated between Hahn coefficients, i.e,, normalized Hahn polynomials of a discrete variable, and generalized 3j symbols, which extend the algebra of quantum mechanical vector coupling to (hyper)angular momenta, in particular allowing for j values multiple of 1/4. The calculation of these coefficients is illustrated, both directly from the defining generalized hypergeometric series F-3(2)(1) and from three-term recursion relationships, the latter particularly useful for large values of the entries. Their role is outlined as matrix elements for the overlap of alternative hyperspherical harmonics (timber coefficients), The semiclassical limit is also investigated, with reference to their use as discrete analogs of hyperspherical harmonics.