论文标题
关于截短的退化钟形多项式的注释
A note on truncated degenerate Bell polynomials
论文作者
论文摘要
本文的目的是引入截短的退化钟形多项式和数字，并研究其某些特性。更详细地，我们获得了明确的表达式，涉及其他特殊多项式的身份，积分表示，类似Dobinski的公式以及生成函数的表达式，以差分运算符和线性不完整的伽马功能。此外，我们引入了截短的退化修饰的钟形多项式和数字，并为这些多项式获得相似的结果。作为结果的应用，我们表明，截断的退化钟数可以表示为有限的总和，涉及β随机变量具有某些参数的矩矩。
The aim of this paper is to introduce truncated degenerate Bell polynomials and numbers and to investigate some of their properties. In more detail, we obtain explicit expressions, identities involving other special polynomials, integral representations, Dobinski-like formula and expressions of the generating function in terms of differential operators and linear incomplete gamma function. In addition, we introduce truncated degenerate modified Bell polynomials and numbers and get similar results for those polynomials. As an application of our results, we show that the truncated degenerate Bell numbers can be expressed as a finite sum involving moments of a beta random variable with certain parameters.
