ABSTRACT
Computing the Wigner matrix elements from the general Wigner equation is notoriously prone to numerical instabilities; one strategy to avoid them is to use recurrence relationships. To this end, a family of recurrence relations can be constructed by performing a reduction of the direct product of two Wigner matrices for the integer and half-integer angular momenta to the sum of two Wigner matrices that have the corresponding raised and lowered angular momentum indices. This chapter describes the derivation that leads to these recurrence relations. In that family, one set of recurrence relations employs increment in the second azimuthal index, whereas the companion set uses increment in the first azimuthal index.
