ABSTRACT

The classical 2-orthogonal polynomials share the so-called Hahn property, this means that they are 2-orthogonal polynomials whose the sequences of their derivatives are also 2-orthogonal polynomials. Based only on this property, a new class of classical 2-orthogonal polynomials is obtained as particular solution of the non-linear system governing the coefficients involved in the recurrence relation fulfilled by these polynomials. A differential-recurrence relation as well as a third-order differential equation satisfied by the resulting polynomials are given. Many interesting subcases are highlighted and explicitly presented with special reference to some connected results that exist in the literature. The integral representations of their associated linear functionals will be exhaustively discussed in a forthcoming publication.

摘要

经典2正交多项式具有所谓的Hahn性质，这意味着它们是2正交多项式，其导数序列也是2正交多项式。仅基于该性质，获得了新的古典2-正交多项式，作为控制这些多项式实现的递归关系中涉及的系数的非线性系统的特定解决方案。给出了所得到的多项式所满足的微分递归关系以及三阶微分方程。突出显示了许多有趣的子案例，并明确引用了文献中存在的一些相关结果。它们的相关线性功能的积分表示将在即将出版的出版物中进行详尽讨论。