  Any nonsingular function of spin j matrices always reduces to a matrix
polynomial of order 2j. The challenge is to find a convenient form for the
coefficients of the matrix polynomial. The theory of biorthogonal systems is a
useful framework to meet this challenge. Central factorial numbers play a key
role in the theoretical development. Explicit polynomial coefficients for
rotations expressed either as exponentials or as rational Cayley transforms are
considered here. Structural features of the results are discussed and compared,
and large j limits of the coefficients are examined.
