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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $ _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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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1013333-4
PII: S 0002-9947(1991)1013333-4
Article copyright: © Copyright 1991 American Mathematical Society