  A one-parameter generalisation R_{\lambda}(X;b) of the symmetric Macdonald
polynomials and interpolations Macdonald polynomials is studied from the point
of view of branching rules. We establish a Pieri formula, evaluation symmetry,
principal specialisation formula and q-difference equation for
R_{\lambda}(X;b). We also prove a new multiple q-Gauss summation formula and
several further results for sl_n basic hypergeometric series based on
R_{\lambda}(X;b).
