通过替换的层次Dobinski型关系和矩问题
Hierarchical Dobinski-type relations via substitution and the moment problem
摘要：
本文研究了由指数玻色子（[a，a*]=1）单项式的正规序exp（x（a*）^ra），r= 1，2，.，在它们的指数生成函数（EGF）的组成下。他们原来是谢弗类型。我们证明了这些序列的两个关键属性仍然保留在替换组合下：（a）Stieltjes矩问题的解决方案的属性;和（b）通过无穷级数（Dobinski型关系）表示这些序列。我们给出了满足性质（a）和（b）的这种组合物的许多例子。我们获得了新的Dobinski型公式，并解决了相关的时刻问题的几个层次定义的组合系列的序列。
英文摘要：
We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.
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