The associated Askey-Wilson polynomials

Ismail, Mourad E. H.; Rahman, Mizan

doi:10.1090/S0002-9947-1991-1013333-4

The associated Askey-Wilson polynomials
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by Mourad E. H. Ismail and Mizan Rahman PDF

Trans. Amer. Math. Soc. 328 (1991), 201-237 Request permission

Abstract:

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.

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