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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Exceptional $q$-Askey-Wilson polynomials and continued fractions
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by Dharma P. Gupta and David R. Masson PDF
Proc. Amer. Math. Soc. 112 (1991), 717-727 Request permission

Abstract:

Two linearly independent solutions of the three-term recurrence relation for the $q$-Askey-Wilson polynomials are obtained for the special cases $abcd = {q^m},m = 1,2, \ldots$.By obtaining the subdominant solution and employing Pincherle’s theorem, the associated continued fractions and properties of the corresponding weight functions are derived. The cases $abcd = q\;{\text {or}}\;{q^2}$ are exceptional. They differ from the cases considered by Askey and Wilson [1 ] and are limits of a family of associated cases considered by Ismail and Rahman [5].
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 717-727
  • MSC: Primary 33D45; Secondary 39A10, 40A15
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1059625-X
  • MathSciNet review: 1059625