论文标题
关于Askey-Wilson多项式的另一个表征
On another characterization of Askey-Wilson polynomials
论文作者
论文摘要
在本文中，我们表明正交多项式的唯一序列$（p_n）_ {n \ geq 0} $满足\ begin \ begin {align*} ϕ（x）\ mathcal {d} _q p_q p_ {n} +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson operator和$ \ Mathcal {s} _Q $平均操作员，是Askey-Wilson多项式的倍数，或它们的特定或限制案例。
In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} ϕ(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson operator and $\mathcal{S}_q$ the averaging operator, are the multiple of Askey-Wilson polynomials, or specific or limiting cases of them.
