In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey-Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. From the terminating basic hypergeometric representations of these polynomials, and due to symmetry in their free parameters, we are able to exhaustively explore the terminating basic hypergeometric transformation formulae which these polynomials satisfy.

中文翻译：

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终止 Askey-Wilson 多项式的基本超几何表示和变换

在这篇综述论文中，我们详尽地探讨了 Askey-Wilson 多项式的终止基本超几何表示以及这些多项式所满足的相应终止基本超几何变换。从这些多项式的终止基本超几何表示，并且由于它们的自由参数的对称性，我们能够详尽地探索这些多项式所满足的终止基本超几何变换公式。