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

- Manuel Alfaro, Juan J. Moreno-Balcazar, Teresa E. Perez, Miguel A. Piñar, Luisa Rezola
- 2001

Let Qn be the polynomials orthogonal with respect to the Sobolev inner product (f; g)S = fg d0 + f g d1; being (0; ;1) a coherent pair where one of the measures is the Hermite measure. The outer relative asymptotics for Qn with respect to Hermite polynomials are found. On the other hand, we consider the Sobolev scaled polynomials and we obtain the… (More)

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)

We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f, g) S = f, g + λf , g where f, g = 1 −1 f (x)g(x)(1 − x 2) α−1/2 dx with α > −1/2 and λ > 0. The asymptotics of the zeros and norms of these polynomials is also established. The study of the orthogonal polynomials with respect to the… (More)

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)

This paper deals with Mehler–Heine type asymptotic formulas for the 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.

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.

1 −1 f (x)g(x)dψ (α,β) (x) + f (x)g (x)dψ(x), where dψ (α,β) (x) = (1 − x) α (1 + x) β dx with α, β > −1, and ψ is a measure involving a rational modification of a Jacobi weight and with a mass point outside the interval (-1,1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product on different regions… (More)