On poly-Bell numbers and polynomials

被引：0

作者：

Guettai, Ghania ^{[1
]}

Laissaoui, Diffalah ^{[2
]}

Rahmani, Mourad ^{[1
]}

Sebaoui, Madjid ^{[2
]}

机构：

[1] USTHB, Fac Math, BP 32, Algiers 16111, Algeria

[2] Dr Yahia Fares Univ Medea, Medea 26000, Algeria

来源：

QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 11期

关键词：

Bell numbers and polynomials; Bernoulli polynomials; generating function; probabilistic representation; Stirling numbers;

D O I：

10.2989/16073606.2020.1805039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, horizontal ellipsis ). 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.

引用

页码：1463 / 1483

页数：21

共 19 条

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