与Hahn差分算子相关的离散正交多项式
Discrete orthogonal polynomials related to Hahn difference operator
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中文总结 AI 辅助
本文研究线性格上的一般离散正交多项式，推导其结构关系及四阶差分方程，并分析半经典与经典特例，给出系数计算示例。
中文摘要 AI 辅助
本文研究了线性格上的一般离散正交多项式序列，包括所谓的离散Laguerre--Hahn正交多项式。我们推导了涉及正交多项式及其伴随多项式的结构关系，以及这些Laguerre--Hahn正交多项式所满足的四阶线性差分方程的显式形式。此外，还分析了对应于半经典和经典正交多项式族的特殊情况，这些情况导致二阶差分方程。文中还给出了几个示例，说明如何为各种正交多项式族计算这些差分方程的显式系数。
英文摘要
This work studies general sequences of discrete orthogonal polynomials on linear lattices, including the so-called discrete Laguerre--Hahn orthogonal polynomials. We deduce the structure relations involving the orthogonal polynomials and their associated, as well as the explicit form of the fourth--order linear difference equation satisfied by these Laguerre--Hahn orthogonal polynomials. Furthermore, the particular cases corresponding to semiclassical and classical families of orthogonal polynomials, which lead to second--order difference equations, are also analyzed. Several examples illustrating the computation of the explicit coefficients of these difference equations for various families of orthogonal polynomials are also presented.
发表机构
- Universidade da Beira Interior（贝拉内陆大学）
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