论文标题
Askey-Wilson多项式的终止串联表示的对称性
Symmetry of terminating series representations of the Askey-Wilson polynomials
论文作者
论文摘要
在本文中，我们探讨了Askey的终止基本高几何序列表示的对称性质 - WILSON多项式以及相应的终止这些多项式满足的基本高几何变换。特别是，我们识别并分类了终止平衡$ {} _ 4 ϕ_3 $的4和7等效类的集合，并终止非常井井有条的$ {} _ 8W_7 $基本超测量系列，与askey-askey-Wilsey-wilson tolynomials连接。我们研究了这些等价类的反转属性，还确定了两组等价类的连接与对称组$ s_6 $，$ s_6 $，终端平衡$ {} _ 4 ϕ_3 $的对称组。然后，我们使用终止平衡$ {} _ 4ϕ_3 $，并终止非常井井有条的$ {} _ 8W_7 $转换，以更广泛地解释Watson的Whipple定理的$ Q $ -Analog及其相反的解释。我们对ASKEY-WILSON多项式的终止基本高几幅序列表示的对称结构进行了广泛的描述。
In this paper, we explore the symmetric nature of the terminating basic hypergeometric series representations of the Askey--Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy. In particular we identify and classify the set of 4 and 7 equivalence classes of terminating balanced ${}_4ϕ_3$ and terminating very-well poised ${}_8W_7$ basic hypergeometric series which are connected with the Askey--Wilson polynomials. We study the inversion properties of these equivalence classes and also identify the connection of both sets of equivalence classes with the symmetric group $S_6$, the symmetry group of the terminating balanced ${}_4ϕ_3$. We then use terminating balanced ${}_4ϕ_3$ and terminating very-well poised ${}_8W_7$ transformations to give a broader interpretation of Watson's $q$-analog of Whipple's theorem and its converse. We give a broad description of the symmetry structure of the terminating basic hypergeometric series representations of the Askey--Wilson polynomials.
