标题： 通过Leonard对理论将双Hahn多项式视为Racah多项式的一种方法 显示英文标题

标题： A way to treat dual Hahn polynomials as Racah polynomials via the theory of Leonard pairs

摘要： 双Hahn多项式$\{u_i(x)\}_{i=0}^d$是一组涉及两个实参数$r$和$s$的离散正交多项式。 令$L,L^*$表示相应的Leonard对。 假设$r\not=0$和$r+s=0$。 我们证明$L,(L^*+\frac{r-d}{2})^{2}$是一个Leonard对。 根据Leonard对的理论，多项式$\{u_i(x)\}_{i=0}^d$不仅是对偶Hahn多项式，而且在相同的内积下也是Racah多项式。 显示英文摘要

摘要： The dual Hahn polynomials $\{u_i(x)\}_{i=0}^d$ are a family of discrete orthogonal polynomials involving two real parameters $r$ and $s$. Let $L,L^*$ denote the corresponding Leonard pair. Assume that $r\not=0$ and $r+s=0$. We show that $L,(L^*+\frac{r-d}{2})^{2}$ is a Leonard pair. According to the theory of Leonard pairs, the polynomials $\{u_i(x)\}_{i=0}^d$ are not only the dual Hahn polynomials but also the Racah polynomials with respect to the same inner product.