arXiv subjects

Mohamed Amine Boutiche

Publications and source records attributed to Mohamed Amine Boutiche.

4 recordsLinked to original sources

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↗

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↗

arXiv2016

Some Aspects of the Wiener Index for Sun Graphs

The Wiener index $W(G)$ is the sum of distances of all pairs of vertices of the graph $G$. The Wiener polarity index $W_{p}(G)$ of a graph $G$ is the number of unordered pairs of vertices $u$ and $v$ of $G$ such that the distance $d_{G}(u,v)$ between $u$ and $v$ is $3$. In this paper the Wiener and the Wiener polarity indices of sun graphs are computed. A relationship between those indices with some other topological indices are presented. Finally, we find the Hosoya (Wiener) polynomial for sun graphs.

math.CO↗