Contiguous relations, continued fractions and orthogonality

We examine a special linear combination of balanced very-well-poised basic hypergeometric series that is known to satisfy a transformation. We call this and show that it satisfies certain three-term contiguous relations. From two of these contiguous relations for 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 -analogue of Ramanujan's Entry 40 continued fraction, and a conjecture of Askey concerning the latter. Some new -series identities are also obtained. One is an important three-term transformation for 's which generalizes all the known two- and three-term transformations. Others are new and unexpected quadratic identities for these very-well-poised 's.