3 citations · 6 across the 8 of their papers we have counts for
9 papers
On a class of Rainville type generating functions for classical orthogonal polynomials
Mohammed Brahim Zahaf, Mohammed Mesk
The aim of this work is to characterize all generating functions of the form for the classical orthogonal polynomials. Further generating functions are also pr…
On a Class of Polynomials Generated by F (xt -- R(t))
Mohammed Mesk, Mohammed Brahim Zahaf
We investigate polynomial sets {P n } n0 with generating power series of the form F (xt -- R(t)) and satisfying, for n 0, the (d + 1)-order recursion xP\_ n (x) = P\_{ n…
A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind
Mohammed Mesk, Mohammed Brahim Zahaf
We show that the only polynomial sets with a generating function of the form F (xt -- R(t)) and satisfying a three-term recursion relation are the monomial set and the rescaled ult…
New kinds of deformed Bessel functions
Mohammed Brahim Zahaf, Dominique Manchon
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equa…
Confluence of singularities of differential equation: a Lie algebra contraction approach
Mohammed Brahim Zahaf, Dominique Manchon
We investigate here the confluence of singularities of Mathieu differential equation by means of the Lie algebra contraction of the Lie algebra of the motion group M(2) on the Heis…
New connection formulae for some q-orthogonal polynomials in q-Askey scheme
Abdelkader Yanallah, Mohammed Brahim Zahaf
New nonlinear connection formulae of the q-orthogonal polynomials, such continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and q-Gegenbauer polynomials, in terms…