论文标题
在第二阶q-差方程中，al-salam-carlitz i-sobolev型多项式高阶
On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
论文作者
论文摘要
此贡献涉及序列$ \ {\ MATHBB {在相应正交间隔的两个边界上涉及任意数量的$ q $衍生品。我们提供了多个版本的相应连接公式，梯形运算符和几个版本的第二阶$ q $ - 差异方程式在此序列中满足。作为对文献的新颖贡献，我们提供了一定的三个术语复发公式，并通过$ \ mathbb {u} _ {n}^{（a）}（x; q，j）$满足的有理系数，这铺平了为所谓的$ j $ fractions建立一个吸引人的属性范围的框架，以建立对bolev-sueboner的框架的范围。
This contribution deals with the sequence $\{\mathbb{U}_{n}^{(a)}(x;q,j)\}_{n\geq 0}$ of monic polynomials, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam--Carlitz I orthogonal polynomials, and involving an arbitrary number of $q$-derivatives on the two boundaries of the corresponding orthogonality interval. We provide several versions of the corresponding connection formulas, ladder operators, and several versions of the second order $q$-difference equations satisfied by polynomials in this sequence. As a novel contribution to the literature, we provide certain three term recurrence formula with rational coefficients satisfied by $\mathbb{U}_{n}^{(a)}(x;q,j)$, which paves the way to establish an appealing generalization of the so-called $J$-fractions to the framework of Sobolev-type orthogonality.
