Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 33A65, 42C05

Retrieve articles in all journals with MSC: 33A65, 42C05

Additional Information

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