On poly-Bell numbers and polynomials
Number Theory
2018-12-12 v1
Abstract
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.
Cite
@article{arxiv.1812.04136,
title = {On poly-Bell numbers and polynomials},
author = {Ghania Guettai and Diffalah Laissaoui and Mourad Rahmani and Madjid Sebaoui},
journal= {arXiv preprint arXiv:1812.04136},
year = {2018}
}
Comments
23 pages