论文标题
部分可观测时空混沌系统的无模型预测
Central factorial numbers associated with sequences of polynomials
论文作者
论文摘要
许多重要的特殊数字出现在某些多项式的扩展中，反之亦然，例如中央阶乘数字，退化中央阶乘数字和中央LAH数字，这些数字最近被引入。在这里，我们将其推广到任何多项式序列。令P为多项式序列的空间，使得多项式的程度小于n。本文的目的是研究与p和p相关的第二种相关的中心阶乘数字，并借助umbral conculus技术，以统一和系统的方式研究。与P相关的中央阶乘数字享有正交性和反相关关系。我们通过许多示例来说明我们的结果，并通过将与P相关的中央阶乘数字应用于我们的每个示例中的中心阶乘数字来获得有趣的正交性和反关系。
Many important special numbers appear in the expansions of some polynomials in terms of central factorials and vice versa, for example central factorial numbers, degenerate central factorial numbers, and central Lah numbers which are recently introduced. Here we generalize this to any sequence of polynomials. Let P be the space of a sequence of polynomials such that the degree of the polynomials less than n . The aim of this paper is to study the central factorial numbers of the second associated with P and of the first kind associated with P, in a unified and systematic way with the help of umbral calculus technique. The central factorial numbers associated with P enjoy orthogonality and inverse relations. We illustrate our results with many examples and obtain interesting orthogonality and inverse relations by applying such relations for the central factorial numbers associated with P to each of our examples.
