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Proceedings of the American Mathematical Society

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



A projection formula for the Askey-Wilson polynomials and an application

Author: Mizan Rahman
Journal: Proc. Amer. Math. Soc. 103 (1988), 1099-1107
MSC: Primary 33A65; Secondary 05A30
MathSciNet review: 954990
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Abstract: A projection formula for $ {p_n}(x;a,b,c,d\vert q)$, the Askey-Wilson polynomials, is obtained by using a generalization of Askey and Wilson's $ q$-beta integral. The result is used to find a $ q$-analogue of the Feldheim-Vilenkin formula for ultraspherical polynomials. A $ q$-analogue of the ultraspherical polynomials, other than the one due to Rogers, is also introduced.

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Keywords: $ q$-ultraspherical and Askey-Wilson polynomials, Feldheim-Vilenkin formula, balanced and very-well-poised basic hypergeometric series
Article copyright: © Copyright 1988 American Mathematical Society