Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials

Nuwacu, Jean Paul; Van Assche, Walter

doi:10.1090/tran/8200

Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
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by Jean Paul Nuwacu and Walter Van Assche PDF

Trans. Amer. Math. Soc. 373 (2020), 8289-8312 Request permission

Abstract:

We first show how one can obtain Al-Salam–Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey–Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey–Wilson, multiple continuous dual $q$-Hahn, and multiple Al-Salam–Chihara polynomials from the multiple little $q$-Laguerre and the multiple little $q$-Jacobi polynomials.

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