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

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.