Limit relations between qq-Krall type orthogonal polynomials

In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a $q$-classical linear functional via the addition of one or two mass points. The limit relations between the $q$-Krall type modification of big $q$-Jacobi, little $q$-Jacobi, big $q$-Laguerre, and other families of the $q$-Hahn tableau are established.Comment: 19 Pages, 3 tables, 1 figur

On the limit of non-standard q-Racah polynomials

The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials such that the orthogonality properties and the three-term recurrence relations remain valid

The q-Racah-Krall-type polynomials

In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the \textit{standard} $q$-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained and some of their limit cases are discussed

On the Krall-type Askey-Wilson Polynomials

In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$. Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as basic hypergeometric series

On the Properties of Special Functions on the linear-type lattices

We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to $q$-classical polynomials are given

Modelos matemáticos en biología: un viaje de ida y vuelta

El objetivo de este trabajo es mostrar la provechosa interacción entre la Biología y la Matemática. Para ello veremos cómo, por una parte, la Matemática es una herramienta sumamente interesante para entender distintos fenómenos biológicos como la dinámica del ADN, el crecimiento de tumores, dinámica de poblaciones, etc., y estos, a su vez, son una fuente de problemas matemáticos difíciles.Ministerio de Educación y CienciaJunta de Andalucí

Second order difference equations for certain families of discrete polynomials

In this paper we will consider two algorithms which allow us to obtain second order linear di erence equations for certain families of polynomials. The corresponding algorithms can be implemented in any computer algebra system in order to obtain explicit expressions of the coe cients of the di erence equations.Dirección General de Enseñanza Superio

On characterizations of classical polynomials

It is well known that the classical families of Jacobi, Laguerre, Hermite, and Bessel polynomials are characterized as eigenvectors of a second order linear differential operator with polynomial coefficients, Rodrigues formula, etc. In this paper we present an unified study of the classical discrete polynomials and q-polynomials of the q-Hahn tableau by using the difference calculus on linear-type lattices. We obtain in a straightforward way several characterization theorems for the classical discrete and q-polynomials of the q-Hahn tableau. Finally, a detailed discussion of the Marcelln et. al. characterization is presented