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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Reproducing kernels and bilinear sums for $ q$-Racah and $ q$-Wilson polynomials


Author: Mizan Rahman
Journal: Trans. Amer. Math. Soc. 273 (1982), 483-508
MSC: Primary 33A65; Secondary 42C05
MathSciNet review: 667157
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Abstract: A five-parameter family of reproducing kernels is constructed for $ q$-Racah polynomials. Special cases for $ q$-Hahn and little $ q$-Jacobi polynomials are considered by selecting the parameters appropriately. Corresponding bilinear sums are also obtained for a whole range of $ q$-orthogonal polynomials. As a special case, some product formulas are obtained for $ q$-Racah and $ q$-Wilson polynomials.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0667157-2
PII: S 0002-9947(1982)0667157-2
Keywords: $ q$-Racah polynomials, $ q$-Wilson polynomials, $ q$-Hahn polynomials, connection relation, bilinear formula, reproducing kernel, very well-poised basic hypergeometric series, balanced basic hypergeometric series, continuous $ q$-Jacobi polynomials, Watson and Bateman-type product formulas
Article copyright: © Copyright 1982 American Mathematical Society