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math.CA2024
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…
math.CA2017
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…
math.CA2016
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…