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].References
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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