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On poly-Bell numbers and polynomials
Quaestiones Mathematicae ( IF 0.7 ) Pub Date : 2020-09-22 , DOI: 10.2989/16073606.2020.1805039
Ghania Guettai 1 , Diffalah Laissaoui 2 , Mourad Rahmani 3 , Madjid Sebaoui 2
Affiliation  

This paper aims to construct a new family of numbers and polynomials which are related to the Bell numbers and polynomials by means of the confluent hypergeometric function. We give various properties of these numbers and polynomials (generating functions, explicit formulas, integral representations, recurrence relations, probabilistic representation,...). We also derive some combinatorial sums including the generalized Bernoulli polynomials, lower incomplete gamma function, generalized Bell polynomials. Finally, by applying Cauchy formula for repeated integration, we introduce poly-Bell numbers and polynomials.

中文翻译:

关于 poly-Bell 数和多项式

本文旨在通过合流超几何函数构造一个新的与贝尔数和多项式相关的数和多项式族。我们给出了这些数字和多项式的各种性质(生成函数、显式公式、积分表示、递推关系、概率表示等)。我们还推导出了一些组合和,包括广义伯努利多项式、下不完全伽马函数、广义贝尔多项式。最后,通过应用柯西公式进行重复积分,我们引入了多贝尔数和多项式。
更新日期:2020-09-22
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