# Hamza ChaggaraUniversity of Sousse | ISTLS · Department of Mathematics

Hamza Chaggara

Professor

## About

22

Publications

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219

Citations

Introduction

## Publications

Publications (22)

In this paper, we introduce a new d-orthogonal polynomial sequence by resolving a characterization problem involving a generalized Dunkl operator. We give some properties of this family, namely, a generating function, the fold symmetry property, a higher-order recurrence relation and differential–difference equation, the inversion formula, the expl...

The main aim of this paper is to introduce and investigate a new d-orthogonal family generalizing the Laguerre polynomial set. We use operational rules associated with corresponding lowering, raising and transfer operators to derive many related properties, namely, recurrence relation, d-orthogonality, functional vector of d-orthogonality, inversio...

In this paper, we give a simple and original method based on inverse relation to express explicitly the linearization coefficients for some general classes of basic hypergeometric polynomial set in terms of the basic Kampé de Fériet function. We use symbolic computation algorithms, namely, q -Multisum to find recurrence relations for the resulting...

In this paper, we are interested in the following problem. We assume that {Pn}n≥0 is a monic 2-orthogonal polynomial sequence and we analyse the existence of a sequence of 2-orthogonal polynomials {Qn}n≥0 such that we have a decomposition Pn(x)=Qn(x)+anQn−1(x),an≠0,n≥1. This constitutes the counterpart in the framework of 2-orthogonality of those a...

In this paper, we characterize the discrete Hahn-classical d-orthogonal polynomial sets (and their iterated) by a difference distributional matrix equation satisfied by the associated d-dimensional functional vector, where the coefficient matrices are explicitly given. As a result we describe this set of polynomials via a structure relation. We ill...

In this work, we show some properties of Sheffer polynomials arising from quasi-monomiality. We survey characterization problems dealing with d-orthogonal polynomial sets of Sheffer type. We revisit some families in the literature and we state an explicit formula giving the exact number of Sheffer type d-orthogonal sets. We investigate, in detail,...

The polynomial sequences of Sheffer type {Pn}n≥0 are defined by the
following generating function:
JG(x,t)= A(t)exp(xC(t)).
In this work, we are interested, with these sequences when they are
also d-orthogonal polynomial sets, that is to say polynomials satisfying
one standard (d + 1)-order recurrence relation. We revisit some
families in the lite...

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric polynomials and we derive expansion formulae corresponding to all the families within the $q$-Askey scheme.

The main purpose of this paper is to study the connection sequence between two polynomial sets. We prove that any two equivalent polynomial sets can be connected with a Sheffer sequence. The principal result presents a unification of some useful known results. The inversion, addition and duplication sequences are considered as particular cases. Mor...

In this work, we prove that the zeros of the hyper-Bessel function are located on rays emanating from the origin with the positive real axis as ray, and that the only d-orthogonal Jensen polynomials associated with an entire function in the Laguerre–Pólya class are the d-orthogonal Laguerre polynomials.

We consider the problem of finding explicit formulas, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. Most of the computations are carried out by the computer algebra system Maple using appropriate algorithms.

This article deals with the problem of finding closed analytical formulae for generalized linearization coefficients for Jacobi polynomials. By considering some special cases, we obtain a reduction formula using for this purpose symbolic computation, in particular Zeilberger’s and Petkovsek’s algorithms.

In this paper, we use operational rules associated with three operators corresponding to a generalized Hermite polynomials introduced by Szegö to derive, as far as we know, new proofs of some known properties as well as new expansions formulae related to these polynomials.

In this paper, we express explicitly the linearization coefficients related to three Boas–Buck polynomial sets using their corresponding generating functions. We apply the obtained results to many classes of polynomials including some generalized hypergeometric polynomials. The corresponding linearization coefficients will be expressed by means of...

In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give clo...

In this paper, a general method to express explicitly connection coefficients between two Boas–Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.

The lowering operator σ associated with a polynomial set
{Pn}n≥0 is an operator not depending on n and satisfying the relation σPn=nPn−1. In this paper, we express explicitly the linearization coefficients for
polynomial sets of Sheffer type using the corresponding lowering
operators. We obtain some well-known results as particular cases.

The lowering operator σ associated with a polynomial set {Pn}n⩾0 is an operator not depending on n and satisfying the relation σ(Pn)=nPn-1. In this paper, we express explicitly the connection coefficients between two polynomial sets using their corresponding lowering operators. We obtain some well-known results as particular cases including some du...

The lowering, raising and transfer operators ; and associated with a polynomial set fPngn are three operators, not depending on n, and satisfying the relations P n = nPn 1; P n = Pn+1 and B n = Pn; n = 0;1;:::; In this talk, we present a general method, based on operational rules with these operators, to study connection and linearization problems....