11 citations · 45 across the 27 of their papers we have counts for
6 papers · 1 filter
On some properties on bivariate Fibonacci and Lucas polynomials
Hacéne Belbachir, Farid Bencherif
In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomia…
Hankel hyperdeterminants, rectangular Jack polynomials and even powers of the Vandermonde
Hacene Belbachir, Adrien Boussicault, Jean-Gabriel Luque
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of J…
A note on calculating autocovariances of periodic ARMA models
Abdelhakim Aknouche Hacène Belbachir Fayçal Hamdi
An analytically simple and tractable formula for the start-up autocovariances of periodic ARMA (PARMA) models is provided.
Sums of products of generalized Fibonacci and Lucas numbers
Hacene Belbachir, Farid Bencherif
In this paper, we establish several formulae for sums and alternating sums of products of generalized Fibonacci and Lucas numbers. In particular, we recover and extend all results…
Unimodality of ordinary multinomials and maximal probabilities of convolution powers of discrete uniform distribution
Hacene Belbachir
We establish the unimodality and the asymptotic strong unimodality of the ordinary multinomials and give their smallest mode leading to the expression of the maximal probability of…
Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution
Hacene Belbachir, Sadek Bouroubi, Abdelkader Khelladi
Using an explicit computable expression of ordinary multinomials, we establish three remarkable connections, with the q-generalized Fibonacci sequence, the exponential partial Bell…