21 citations · 31 across the 9 of their papers we have counts for
8 papers · 1 filter
On the number of non-real zeroes of a homogeneous differential polynomial and a generalization of the Laguerre inequalities
Mikhail Tyaglov, Mohamed J. Atia
Given a real polynomial with only real zeroes, we find upper and lower bounds for the number of non-real zeroes of the differential polynomial $$ F_{\varkappa}[p](z):= p(z)p''(…
Trajectories of a quadratic differential related to a quasi-exactly solvable sextic oscillator
Mohamed Jalel Atia, Wafaa Karrou, Mondher Chouikhi +1
In this paper, we discuss the existence of solution (as Cauchy transform of a signed measure) of a particular algebraic quadratic equation of the form $\mathcal{C}^{2}\left( z\righ…
Algebraic equation and quadratic differential related to generalized Bessel polynomials with varying parameters
Mohamed Jalel Atia, Faouzi Thabet
The limiting set of zeros of generalized Bessel polynomials with varying parameters depending on the degree n cluster in a curve on the complex plane, which is a finite critical tr…
Zeros of polynomials orthogonal with respect to a signed weight
M. Benabdallah, M. J. Atia, R. S. Costas-Santos
In this paper we consider the polynomial sequence that is orthogonal on with respect to the weight function $x^{2q+1}(1-x^{2})^α(1-x), α>-1, q\in \mathb…
Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform
Mohamed Jalel Atia, Faouzi Thabet
In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a…
Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters
M. J. Atia, A. Martinez-Finkelshtein, P. Martinez-Gonzalez +1
In this paper we study the asymptotics (as ) of the sequences of Laguerre polynomials with varying complex parameters depending on the degree . More precisely,…
An explicit formula for the linearization coefficients of Bessel polynomials II
Mohamed Jalel Atia
In this paper, a single sum formula for the linearization coefficients of the Bessel polynomials is given. In three special cases this formula reduces indeed to either Atia and Zen…
An explicit formula for the linearization coefficients of Bessel polynomials
Mohamed Jalel Atia, Jiang Zeng
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formul…