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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 328 (1991), 201-237
  • MSC: Primary 33C50; Secondary 42C05
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1013333-4
  • MathSciNet review: 1013333