Jacobi-Type orthogonal polynomials: holonomic equation and electrostatic interpretation

16 pages, no figures.-- MSC2000 code: 33C47.MR#: MR2410226 (2009c:33029)In this contribution we study some pertubation of the Jacobi weight function by adding a mass point at x = 1, one of the ends of the interval supporting such a measure. We find the explicit expression of the corresponding orthogonal polynomials as well as the holonomic equation that such polynomials satisfy. Next, we analyze the location of their zeros and, finally, we give an electrostatic interpretation of them.The work of the second author (FM) has been supported by Dirección General de investigación, Ministerio de Educación y Ciencia of Spain, grant MTM2006-13000-C03-02.Publicad

Perturbations of Laguerre-Hahn functional: modification by the derivative of a Dirac delta

19 pages, no figures.-- MSC2000 code: 33C47.MR#: MR2492206 (2010a:33031)Zbl#: Zbl pre05509604In this paper, we consider a perturbation of a Laguerre-Hahn functional by adding a derivative of a Dirac delta. This transformation leaves invariant the family of Laguerre-Hahn linear functionals. We shall also analyse the class of the perturbed linear functional. Finally, we illustrate these perturbations by adding the derivative of a Dirac delta to the first kind associated functional of the classical Laguerre functional. The expression of the new orthogonal polynomials is obtained.The work of the first and second author has been supported by Comunidad de Madrid-Universidad Carlos III de Madrid, grant CCG07-UC3M/ESP-3339. The work of the second author has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, grant MTM2006-13000-C03-02.Publicad

Sobre (1, 1) pares coherentes simétricos y polinomios ortogonales Sobolev: un algoritmo para calcular coeficientes de Fourier

In the pioneering paper [13], the concept of Coherent Pair was introduced by Iserles et al. In particular, an algorithm to compute Fourier Coefficients in expansions of Sobolev orthogonal polynomials defined from coherent pairs of measures supported on an infinite subset of the real line is described. In this paper we extend such an algorithm in the framework of the so called Symmetric (1, 1)-Coherent Pairs presented in [8].En el artículo pionero [13], fue introducido el concepto de Par Coherente por Iserles et al. En particular, allí es descrito un algoritmo para calcular coeficientes de Fourier de expansiones de polinomios ortogonales de tipo Sobolev definidos a partir de pares de medidas coherentes soportadas en un subconjunto infinito de la recta real. En esta contribución extendemos tal algoritmo en el contexto de los llamados Pares Simétricos (1, 1)−Coherentes presentados en [8]