论文标题
$ Q $ -HAHN类型的合理功能的双光谱和生物表达性
Bispectrality and biorthogonality of the rational functions of $q$-Hahn type
论文作者
论文摘要
我们介绍了关于$ Q $ - hypherementric分布的理性功能的家庭。 $ q $ -difference运营商$ x $，$ y $，$ z $的三重态显示出与正交多项式的双光谱运算符相似的角色。复发关系和差异方程采用涉及三个操作员的广义特征值问题的形式。 $ x $，$ y $，$ z $生成的代数类似于Askey的代数 - 在正交多项式的情况下。提出了这些操作员的行动。还讨论了与Wilson的$ {} _ {10} ϕ_9 $生物双歧合理函数的连接。
We introduce families of rational functions that are biorthogonal with respect to the $q$-hypergeometric distribution. A triplet of $q$-difference operators $X$, $Y$, $Z$ is shown to play a role analogous to the pair of bispectral operators of orthogonal polynomials. The recurrence relation and difference equation take the form of generalized eigenvalue problems involving the three operators. The algebra generated by $X$, $Y$, $Z$ is akin to the algebras of Askey--Wilson type in the case of orthogonal polynomials. The actions of these operators in three different basis are presented. Connections with Wilson's ${}_{10}ϕ_9$ biorthogonal rational functions are also discussed.
