The associated Askey-Wilson polynomials

Authors:
Mourad E. H. Ismail and Mizan Rahman

Journal:
Trans. Amer. Math. Soc. **328** (1991), 201-237

MSC:
Primary 33C50; Secondary 42C05

MathSciNet review:
1013333

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Abstract: We derive some contiguous relations for very well-poised 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 series and find the weight functions.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1013333-4

Article copyright:
© Copyright 1991
American Mathematical Society