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

Author:
Mizan Rahman

Journal:
Trans. Amer. Math. Soc. **273** (1982), 483-508

MSC:
Primary 33A65; Secondary 42C05

DOI:
https://doi.org/10.1090/S0002-9947-1982-0667157-2

MathSciNet review:
667157

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Abstract | References | Similar Articles | Additional Information

Abstract: A five-parameter family of reproducing kernels is constructed for -Racah polynomials. Special cases for -Hahn and little -Jacobi polynomials are considered by selecting the parameters appropriately. Corresponding bilinear sums are also obtained for a whole range of -orthogonal polynomials. As a special case, some product formulas are obtained for -Racah and -Wilson polynomials.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0667157-2

Keywords:
-Racah polynomials,
-Wilson polynomials,
-Hahn polynomials,
connection relation,
bilinear formula,
reproducing kernel,
very well-poised basic hypergeometric series,
balanced basic hypergeometric series,
continuous -Jacobi polynomials,
Watson and Bateman-type product formulas

Article copyright:
© Copyright 1982
American Mathematical Society