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Proceedings of the American Mathematical Society

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



Exceptional $ q$-Askey-Wilson polynomials and continued fractions

Authors: Dharma P. Gupta and David R. Masson
Journal: Proc. Amer. Math. Soc. 112 (1991), 717-727
MSC: Primary 33D45; Secondary 39A10, 40A15
MathSciNet review: 1059625
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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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Keywords: Askey-Wilson polynomials, three-term recurrence, subdominant solution, Pincherle's theorem, continued fractions, weight functions, mass points
Article copyright: © Copyright 1991 American Mathematical Society