论文标题
在多项式高组上较高等级的力矩函数
Moment functions of higher rank on polynomial hypergroups
论文作者
论文摘要
在本文中，我们考虑了高阶的广义力矩功能。这些功能与二项式类型的众所周知功能密切相关，这些功能已在各种抽象结构上进行了研究。在我们以前的论文中，我们研究了高阶在交换组上的广义力矩功能的特性。特别是，我们证明了在交换群体上的广义力矩功能的表征，是多元钟形多项式和序列添加函数的指数和组成的乘积。在本文中，我们继续研究更抽象的环境中高阶的通用力矩函数序列，即我们考虑在高组上定义的功能。我们通过一个多项式组成的部分衍生物在一个变量的多项式高群上表征了这些函数，从而产生多项式高群和分析函数。例如，我们给出了一个明确的公式，用于在Tchebyshev HyperGroup上最多最多的等级函数。
In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. In our former paper we investigated the properties of generalized moment functions of higher order on commutative groups. In particular, we proved the characterization of generalized moment functions on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and a sequence additive functions. In the present paper we continue the study of generalized moment function sequences of higher order in the more abstract setting, namely we consider functions defined on a hypergroup. We characterize these functions on the polynomial hypergroup in one variable by means of partial derivatives of a composition of polynomials generating the polynomial hypergroup and an analytic function. As an example, we give an explicit formula for moment generating functions of rank at most two on the Tchebyshev hypergroup.
