arXiv subjects

Ghania Guettai

Publications and source records attributed to Ghania Guettai.

4 recordsLinked to original sources

arXiv2024

The Hankel determinants for the generalized derangement polynomials of order r

This paper sets out to introduce the generalized derangement polynomials of order $r $. It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement polynomials of order $ r$. Additionally, the paper offers a probabilistic approach for the generalized derangement polynomials of order $r $. Furthermore, it furnishes a clear expression for the Hankel determinants pertaining to these generalized derangement polynomials of order $r$, and subsequently infers the Hankel determinants for derangement polynomials of the same order, as well as for the count of cyclic derangements.

math.CO↗

arXiv2023

On Certain Recurrence Relations for Generalized Poly-Cauchy Numbers and Polynomials

The main objective of this paper is to present recurrence relations for the generalized poly-Cauchy numbers and polynomials. This is accomplished by introducing the concept of generalized m-poly-Cauchy numbers and polynomials. Additionally, the paper delves into the discussion of the corresponding generalized m-poly-Bernoulli numbers and polynomials that are associated with the aforementioned generalized m-poly-Cauchy numbers and polynomials.

math.NT↗

arXiv2022

Generalized Fubini transform with two variables

In the present paper, we define the generalized Kwang-Wu Chen matrix. Basic properties of this generalization, such as explicit formulas and generating functions are presented. Moreover, we focus on a new class of generalized Fubini polynomials. Then we discuss their relationship with other polynomials such as Fubini, Bell, Eulerian and Frobenius-Euler polynomials. We have also investigated some basic properties related to the degenerate generalized Fubini polynomials.

math.CO↗

arXiv2018

On poly-Bell numbers and polynomials

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.

math.NT↗