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- Manuel Alfaro, Juan J. Moreno-Balcázar, M. Luisa Rezola
- Journal of Approximation Theory
- 2003

Let S n be polynomials orthogonal with respect to the inner product

- Francisco Marcellán, Juan J. Moreno-Balcázar
- Journal of Approximation Theory
- 2001

- Alicia Cachafeiro, Francisco Marcellán, Juan J. Moreno-Balcázar
- Journal of Approximation Theory
- 2003

In this paper we consider a Sobolev inner product (f, g) S = f gdµ + λ f g dµ (1) and we characterize the measures µ for which there exists an algebraic relation between the polynomials, {P n }, orthogonal with respect to the measure µ and the polynomials, {Q n }, orthogonal with respect to (1), such that the number of involved terms does not depend on the… (More)

- Manuel Alfaro, Ana Peña, M. Luisa Rezola, Juan J. Moreno-Balcázar
- Asymptotic Analysis
- 2010

We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we… (More)

- Manuel Alfaro, Juan J. Moreno-Balcázar, Ana Peña, M. Luisa Rezola
- Journal of Approximation Theory
- 2011

This paper deals with Mehler-Heine type asymptotic formulas for so called discrete Sobolev orthogonal polynomials whose continuous part is given by Laguerre and generalized Hermite measures. We use a new approach which allows to solve the problem when the discrete part contains an arbitrary (finite) number of mass points.

- Eliana Xavier Linhares de Andrade, Cleonice F. Bracciali, Laura Castaño-García, Juan J. Moreno-Balcázar
- Journal of Approximation Theory
- 2010

Inner products of the type f, g S = f, g ψ 0 + f , g ψ 1 , where one of the measures ψ 0 or ψ 1 is the measure associated with the Jacobi polynomials, are usually referred to as Jacobi-Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Jacobi-Sobolev inner products. The inner… (More)

- Juan F. Mañas-Mañas, Francisco Marcellán, Juan J. Moreno-Balcázar
- Applied Mathematics and Computation
- 2013

- Cleonice F. Bracciali, Juan J. Moreno-Balcázar
- Applied Mathematics and Computation
- 2015

We obtain the asymptotic behavior of the zeros of a class of generalized hypergeometric polynomials. For this purpose, we make use of a Mehler–Heine type formula for these polynomials. We illustrate these results with numerical experiments and some figures.

In this expository paper we present a survey about asymptotic properties of Sobolev type orthogonal polynomials with unbounded support.

- Bujar Xh. Fejzullahu, Francisco Marcellán, Juan J. Moreno-Balcázar
- Journal of Approximation Theory
- 2013