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.

中文翻译：

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多重 Askey-Wilson 多项式和相关的基本超几何多重正交多项式

我们首先展示了如何从小 $q$-Laguerre 和小 $q$-Jacobi 多项式中获得 Al-Salam--Chihara 多项式、连续对偶 $q$-Hahn 多项式和 Askey--Wilson 多项式转换。然后扩展这个过程以从多个小 $q$-Laguerre 和多个小 $q$-Jacobi 多项式中获得多个 Askey--Wilson、多个连续对偶 $q$-Hahn 和多个 Al-Salam--Chihara 多项式.