q-trinomial identities

We obtain connection coefficients between q-binomial and q-trinomial coeffi cients. Using these, one can transform q-binomial identities into q-trinomi al identities and back again. To demonstrate the usefulness of this procedu re we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which hav e recently arisen in their study of the phi(2,1) and phi(1,5) perturbations of minimal conformal field theory. (C) 1999 American Institute of Physics. [S0022-2488(99)01105-6].