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

Rahman, Mizan

doi:10.1090/S0002-9947-1982-0667157-2

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

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

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

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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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