  We examine a special linear combination of balanced very-well-poised $\tphia$
basic hypergeometric series that is known to satisfy a transformation. We call
this $\Phi$ and show that it satisfies certain three-term contiguous relations.
From two sets of contiguous relations for $\Phi$ we obtain fifty-six pairwise
linearly independent solutions to a three-term recurrence that generalizes the
recurrence for Askey-Wilson polynomials. The associated continued fraction is
evaluated using Pincherle's theorem. From this continued fraction we are able
to derive a discrete system of biorthogonal rational functions. This ties
together Wilson's results for rational biorthogonality, Watson's $q$-analogue
of Ramanujan's Entry 40 continued fraction and a conjecture of Askey concerning
the latter. Some new $q$-series identities are also obtained. One is an
important three-term transformation for $\Phi$'s which generalizes all the
known two and three-term $\ephis$ transformations. Others are new and
unexpected quadratic identities for these very-well-poised $\ephis$'s.
