指数Riordan群的一些性质及应用

Some Algebraic Properties and Applications on Exponential Riordan Group

在指数Riordan群定义的基础上得到其行和的计算公式、Euler变换形式以及元素之间的递归关系等性质,并且结合Hermite多项式推导得出一个新的组合恒等式.在应用方面,讨论了用涉及指数族的二项式序列φi(x)定义的广义Pascal函数矩阵,对已有的结论利用Rior-dan阵理论给出了简单的新证明,使得被广泛研究的Pascal矩阵、Pascal函数矩阵的一些性质成为推论.此外,还讨论了元素为Bell多项式的Bell矩阵Bn,给出其指数Riordan阵形式,进而给出了Bn元素所满足的递归关系.

Based on the definition of Exponential Riordan Group, row summation formula, Euler transformation and the recurrence relations satisfied by its elements are obtained in this article. Moreo- ver,a new identity related Hermite polynomials is established. On applications of Exponential Riordan Group, the generalized Pascal matrices is studied, which is defined by the polynomial of binomial type with respect to Exponential Family. A simple new proof to results is displayed by using the theory of Riordan array. In addition,Bell matrices is defined. The recurrence relations satisfied by the elements of Bn is obtained.