We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distribu...

In this paper we consider the oscillation of the delay difference equation with oscillating coefficients x,,+l x. + 2p,(n):z’._k.. 0, n 0. Some comparison and oscillation results are obtained.

In this communication a general kind of simplex partitions are studied. These partitions are associated to some recurrence relations. The study of these equations lead us to set some properties in 2D and 3D about the average adjacencies of the topological entities defining the mesh, when the number of refinements tends to infinite. We prove that this limit is independent of the considered parti...

By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether’s Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not d...

We prove a result on the existence of periodic solutions of a class of systems of differentialdifference equations partially solved with respect to the first-order derivative by constructing it in a form of a series.

Our aim in this paper is to obtain sufficient conditions for the oscillation of every solution of first order difference equations xn+1 − xn + m ∑ i=1 (pixn−ki − qixn−li) = 0, n = 0, 1, 2, ... and xn+1 − xn + m ∑ i=1 (pixn+ki − qixn+li) = 0, n = 0, 1, 2, ... where pi, qi ∈ R and ki, li ∈ N for i = 1, 2, . . . ,m.

The asymptotic contracted measure of zeros of a large class of orthogonal polynomials is explicitly given in the form of a Lauricella function. The polynomials are defined by means of a three-term recurrence relation whose coefficients may be unbounded but vary regularly and have a different behaviour for even and odd indices. Subclasses of systems of orthogonal polynomials having their contrac...

*Correspondence: [email protected] 1Modern Business and Management Department, Guangdong Construction Polytechnic, Guangzhou, 510440, China Full list of author information is available at the end of the article Abstract In this paper, we investigate the solutions of boundary value problems for second-order p-Laplacian difference equations. By using the critical point theory, the existence and mul...

Starting from the D!-Riccati Diierence equation satissed by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourth-order diierence equation satissed by the associated of any integer order of orthogonal polynomials of the-Laguerre-Hahn class. Moreover, in classical situations (Meixner, Charlier, Krawtchouk and Hahn), we give these dii...