论文标题
退化二项式和退化泊松随机变量
Degenerate binomial and degenerate Poisson random variables
论文作者
论文摘要
本文的目的是研究与LAH贝尔多项式相关的泊松随机变量，以及变性的二项式和退化泊松随机变量 与退化的lah-bell多项式。除其他事项外，我们表明，具有参数α的变性泊松随机变量的上升阶乘力矩由在α上评估的退化LAH贝尔多项式给出。我们还表明，退化泊松随机变量的概率生成函数等于退化的lah贝尔多项式的生成函数。此外，我们显示了泊松随机变量的相似结果。在这里，第n个lah-bell数量计算了一组n个元素可以分配到非空的线性订购子集的方式，lah-bell多项式是lah贝尔数的自然扩展，而退化的lah-bell bell bell多项式是lah bell bell bellymials的变性版本。
The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other things, we show that the rising factorial moments of the degenerate Poisson random variable with parameter α are given by the degenerate Lah-Bell polynomials evaluated at α. We also show that the probability-generating function of the degenerate Poisson random variable is equal to the generating function of the degenerate Lah-Bell polynomials. Also, we show similar results for the Poisson random variables. Here the nth Lah-Bell number counts the number of ways a set of n elements can be partitioned into non-empty linearly ordered subsets, the Lah-Bell polynomials are natural extensions of the Lah-Bell numbers and the degenerate Lah-Bell polynomials are degenerate versions of the Lah-Bell polynomials.
