arXiv subjects

J. J. Moreno-Balcázar

Publications and source records attributed to J. J. Moreno-Balcázar.

3 recordsLinked to original sources

arXiv2026

Discrete orthogonal polynomials related to Hahn difference operator

This work studies general sequences of discrete orthogonal polynomials on linear lattices, including the so-called discrete Laguerre--Hahn orthogonal polynomials. We deduce the structure relations involving the orthogonal polynomials and their associated, as well as the explicit form of the fourth--order linear difference equation satisfied by these Laguerre--Hahn orthogonal polynomials. Furthermore, the particular cases corresponding to semiclassical and classical families of orthogonal polynomials, which lead to second--order difference equations, are also analyzed. Several examples illustrating the computation of the explicit coefficients of these difference equations for various families of orthogonal polynomials are also presented.

math.CA↗

arXiv2018

Linearization and Krein-like functionals of hypergeometric orthogonal polynomials

The Krein-like $r$-functionals of the hypergeometric orthogonal polynomials $\{p_{n}(x) \}$ with kernel of the form $x^{s}[ω(x)]^βp_{m_{1}}(x)\ldots p_{m_{r}}(x)$, being $ω(x)$ the weight function on the interval $Δ\in\mathbb{R}$, are determined by means of the Srivastava linearization method. The particular $2$-functionals, which are particularly relevant in quantum physics, are explicitly given in terms of the degrees and the characteristic parameters of the polynomials. They include the well-known power moments and the novel Krein-like moments. Moreover, various related types of exponential and logarithmic functionals are also investigated.

math-ph↗

arXiv2010

The semiclassical--Sobolev orthogonal polynomials: a general approach

We say that the polynomial sequence $(Q^{(λ)}_n)$ is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product $$ _S=<{\bf u} ,{p\, r}> +λ<{\bf u}, {{\mathscr D}p \,{\mathscr D}r}>, $$ where ${\bf u}$ is a semiclassical linear functional, ${\mathscr D}$ is the differential, the difference or the $q$--difference operator, and $λ$ is a positive constant. In this paper we get algebraic and differential/difference properties for such polynomials as well as algebraic relations between them and the polynomial sequence orthogonal with respect to the semiclassical functional $\bf u$. The main goal of this article is to give a general approach to the study of the polynomials orthogonal with respect to the above nonstandard inner product regardless of the type of operator ${\mathscr D}$ considered. Finally, we illustrate our results by applying them to some known families of Sobolev orthogonal polynomials as well as to some new ones introduced in this paper for the first time.

math.CA↗