The last of the hypergeometric continued fractions

A contiguous relation for complementry pairs of very well poised balanced ${}_{10}ϕ_9$ basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan's Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there are systems of biorthogonal rational functions that have yet to be derived.

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