Contiguous relations, continued fractions and orthogonality: An 8Ø 7 model

Abstract

A contiguous relation for very well poised 8ø7 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. When the continued fraction terminates, it has a singularity structure of simple poles which can be associated with a system of biorthogonal rational functions having a discrete weight function. However, in the nonterminating case, the continued fraction does not have explicit singularities and thus we are unable to exhibit the associated orthogonality. This is the first example of this type that we have encountered.