First-order non-homogeneousq-difference equation for Stieltjes function characterizingq-orthogonal polynomials

Orthogonal matrix polynomials satisfying second order difference equations

We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .

A method for solving first order fuzzy differential equation

The Fourth-order Difference Equation Satisfied by the Associated Orthogonal Polynomials of the Delta-Laguerre-Hahn Class

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...

On Fourth-order Difference Equations for Orthogonal Polynomials of a Discrete Variable: Derivation, Factorization and Solutions

We derive and factorize the fourth-order difference equations satisfied by orthogonal polynomials obtained from some modifications of the recurrence coefficients of classical discrete orthogonal polynomials such as: the associated, the general co-recursive, co-recursive associated, co-dilated and the general co-modified classical orthogonal polynomials. Moreover, we find four linearly independe...

Positive Periodic Solutions of Singular First Order Functional Difference Equation

In this paper, we consider the following singular first order functional difference equation Δx(k) = −a(k)x(k) + λb(k)f(x(k − τ(k))), k ∈ Z where f(.) is singular at x = 0. By using a Kranoselskii fixed point theorem, we will establish the existence and multiplicity of positive periodic solutions for the above problem. The results obtained are new, and some examples are given to illustrate our ...