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

DOI:
https://doi.org/10.1090/S0002-9939-1991-1059625-X

MathSciNet review:
1059625

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Abstract | References | Similar Articles | Additional Information

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

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