Angular and hyperangular momentum recoupling, harmonic superposition and Racah polynomials: a recursive algorithm

Generalized 6j symbols are defined in terms of orthonormalized Racah polynomials of a discrete variable and given explicitly as hypergeometric 4F3(1) series. They extend the recoupling coefficients of ordinary angular momentum algebra, including multiples of 1/4 as quantum numbers. A three-term recurrence relationship is exploited for extensive calculations and illustration of their properties. Their role is outlined as matrix elements for superpositions (or overlaps) both between alternative spherical and hyperspherical harmonics and between alternative Sturmian sets, an important case being that of four-dimensional harmonics of S3, which apply to the momentum-space hydrogen atom orbitals.