Moment representations of exceptional X 1 orthogonal polynomials
Moment representations of exceptional X 1 orthogonal polynomials
复制标题
异常 X 1 正交多项式的矩表示
DOI：
10.1016/j.jmaa.2017.05.037
复制
发表时间：
2017
影响因子：
1.3
通讯作者：
Osborn, John
中科院分区：
文献类型：
--
作者：
Kelly, Jessica Stewart;Liaw, Constanze;Osborn, John
我们推广的表示X1例外正交多项式通过行列式的矩阵，有一定的调整矩作为条目。我们直接从达布变换开始，允许一个普遍的观点，而不是依赖于特定系统（雅可比或拉盖尔多项式类型）。我们包括一个递归公式调整的时刻，并提供每个系统的初始调整的时刻。在整个过程中，我们涉及到的各种例子X1例外正交多项式。我们特别关注并提供完整的证明Jacobi和III型Laguerre的情况下，因为它们在文献中不太普遍。最后，我们包括一个初步的讨论，解释更高的余维设置变得更加复杂。可能性和选择的数量是示例性的，但只是开始，缺乏一个规范的标志。
We generalize the representations of X 1 exceptional orthogonal polynomials through determinants of matrices that have certain adjusted moments as entries. We start out directly from the Darboux transformation, allowing for a universal perspective, rather than one dependent upon the particular system (Jacobi or Type of Laguerre polynomials). We include a recursion formula for the adjusted moments and provide the initial adjusted moments for each system. Throughout we relate to the various examples of X 1 exceptional orthogonal polynomials. We especially focus on and provide complete proofs for the Jacobi and the Type III Laguerre case, as they are less prevalent in literature. Lastly, we include a preliminary discussion explaining that the higher codimension setting becomes more involved. The number of possibilities and choices is exemplified, but only starts, with the lack of a canonical flag.