The Associated Askey-Wilson Polynomials
Mourad E. H. Ismail, Mizan Rahman · Transactions of the American Mathematical Society · 1991
We derive some contiguous relations for very well-poised $_8{\phi _7}$ series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials. We then use these solutions to find explicit representations of two families of associated Askey-Wilson polynomials. We identify the corresponding continued fractions as quotients of two very well-poised $_8{\phi _7}$ series and find the weight functions.