  We obtain new explicit formulas for the recurrence coefficients of the
q-orthogonal polynomial sequences in a class that extends the q-Askey scheme.
  Our formulas express the recurrence coefficients in terms of four parameters
that determine the zeroes and poles. By direct substitution of particular
values for the four parameters we obtain all the polynomial sequences in the
q-Askey scheme, including the Askey-Wilson and the Racah polynomials. We also
obtain some families of sequences that may be new.
