Abstract:Exceptional Laguerre and Jacobi polynomials are bispectral, in the sense that as functions of the continuous variable , they are eigenfunctions of a second order differential operator and as functions of the discrete variable , they are eigenfunctions of a higher order difference operator (the one defined by any of the recurrence relations they satisfy). In this paper, under mild conditions on the sets of parameters, we characterize the algebra of difference operators associated to the higher order recurrence relations satisfied by the exceptional Laguerre and Jacobi polynomials.

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中文翻译：

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例外Laguerre和Jacobi多项式的递归关系的代数

摘要：出色的Laguerre和Jacobi多项式是双谱的，在某种意义上，它们是连续变量的函数，是二阶微分算子的本征函数，而作为离散变量的函数，是高阶差分算子的本征函数（一个由他们满足的任何重复关系定义）。在本文中，在温和条件下的参数集上，我们刻画了与异常Laguerre和Jacobi多项式满足的高阶递归关系相关的差分算子的代数。

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