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

## TL;DR

This paper develops a method to derive multiple Askey-Wilson and related polynomials from simpler multiple orthogonal polynomials using special transformations, expanding the theory of basic hypergeometric multiple orthogonal polynomials.

## Contribution

It introduces a novel transformation approach to generate multiple Askey-Wilson and related polynomials from multiple little q-polynomials, extending the classical univariate theory.

## Key findings

- Derived multiple Askey-Wilson polynomials from multiple little q-Laguerre polynomials.
- Extended transformation techniques to obtain multiple continuous dual q-Hahn and Al-Salam--Chihara polynomials.
- Established a systematic method for generating complex multiple orthogonal polynomials from simpler bases.

## 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.