AI 中文总结
该研究提出基于Geronimus变换的统一构造方法，以广义厄米特多项式为例推导各类正交多项式的零点位置、递推关系与微分方程等结果，覆盖多种正交多项式类型。
AI 中文摘要
我们提出一种统一的Geronimus型构造方法，可得到不定正交多项式、例外正交多项式、更一般的缺项正交多项式及多重正交多项式等各类正交多项式。我们以广义厄米特多项式为例说明该思路，并针对Geronimus型变换得到零点位置、递推关系和微分方程等各类结果。
英文摘要
We present a unified Geronimus-type construction that leads to various orthogonal polynomials including indefinite orthogonal polynomials, exceptional and, more generally, lacunary orthogonal polynomials, and multiple orthogonal polynomials. We use generalized Hermite polynomials to demonstrate the idea and obtain various results for the Geronimus-type transformation such as zero location, recurrence relations, and differential equations.
