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Mourad Rahmani

Publications and source records attributed to Mourad Rahmani.

11 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↗
arXiv2023

Recurrences for values of the Hurwitz type poly-Bernoulli numbers and polynomials

The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials. By introducing a new generalization of the Stirling numbers of the second kind, we succeed to establish some combinatorial formulas for the generalized Hurwitz type poly-Bernoulli numbers and polynomials with negative upper indices. Moreover, we give a connection between the generalized Stirling numbers of the second kind and graph theory.

math.CO↗
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↗
arXiv2017

On the higher derivatives of the inverse tangent function

In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating functions, recurrence relations and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas and Matching polynomials are established.

math.CA↗
arXiv2017

A closed formula for the generating function of p-Bernoulli numbers

In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving Stirling numbers of the second kind.

math.NT↗
arXiv2012

Some results on Whitney numbers of Dowling lattices

In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is relation between Stirling and Eulerian polynomials. Can we find a new relation between Dowling polynomials and other polynomials generalizing Eulerian polynomials? In addition, some congruences for the Dowling numbers are given.

math.CO↗
arXiv2012

Generalized Stirling transform

In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which generalizes the usual Stirling transform and investigate the corresponding generating functions also. In addition, some interesting consequences of these results related to classical sequences like Fibonacci, Bernoulli and the numbers of derangements have been derived.

math.CO↗