Exceptional -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 -Askey-Wilson polynomials are obtained for the special cases .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 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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1059625-X

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