Edmundo J. Huertas Cejudo

Publications (9) View all

• Article: Strong and ratio asymptotics for Laguerre polynomials revisited

  Alfredo Deaño, Edmundo J. Huertas, Francisco Marcellán
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  ABSTRACT: In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the context of Krall-Laguerre or Laguerre-Sobolev-type orthogonal polynomials, are notoriously difficult to compute. In this paper, we propose the use of an alternative expansion, due to Buchholz, in terms of Bessel functions of the first kind. The coefficients in this expansion can be obtained in a straightforward way using symbolic computation. As an application, we derive extra terms in the asymptotic expansion of ratios of Laguerre polynomials in $C\[0,\infty)$.
  Journal of Mathematical Analysis and Applications 07/2013; 403(2):477--486. · 1.00 Impact Factor
• Article: A Finite Class of Orthogonal Functions Generated by Routh-Romanovski Polynomials

  Mohammad Masjed-Jamei, Francisco Marcellán, Edmundo J. Huertas
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  ABSTRACT: It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh–Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.
  Complex Variables and Elliptic Equations 09/2012; · 0.53 Impact Factor
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  Article: Asymptotic properties of Laguerre–Sobolev type orthogonal polynomials

  Herbert Dueñas, Edmundo Huertas, Francisco Marcellán
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  ABSTRACT: In this contribution we consider the asymptotic behavior of sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product <p,q>S=int_0^infty p(x)q(x)x^alpha e^-xdx+Np^prime (a)q^prime (a),alpha >-1 $$ where N ∈ ℝ + , and a ∈ ℝ − . We study the outer relative asymptotics of these polynomials with respect to the standard Laguerre polynomials. The analogue of the Mehler–Heine formula as well as a Plancherel–Rotach formula for the rescaled polynomials are given. The behavior of their zeros is also analyzed in terms of their dependence on N .
  Numerical Algorithms 12/2012; 60(1):51-73. · 1.04 Impact Factor
• Article: An electrostatic model for zeros of perturbed Laguerre polynomials

  Edmundo J. Huertas, Francisco Marcellán, Héctor Pijeira
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  ABSTRACT: In this paper we consider the sequences of polynomials orthogonal with respect to the Laguerre measure modified by m Dirac mass points located in the negative real semiaxis. We first focus our attention in the representation of these polynomials in terms of the standard Laguerre polynomials. Next we find the explicit formula for their outer relative asymptotics, as well as the holonomic equation that such polynomials satisfy. Finally, an electrostatic interpretation of their zeros in terms of a logarithmic potential is presented.
  Proceedings of the American Mathematical Society 07/2012; · 0.61 Impact Factor
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  Thesis: Analytic Properties of Krall-type and Sobolev-type Orthogonal Polynomials

  Edmundo J. Huertas Cejudo
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  ABSTRACT: This thesis is focused on the so called standard and nonstandard families of orthogonal polynomials. We begin by giving a brief historical introduction and some preliminary concepts about orthogonal polynomial sequences. The first part of the memoir is devoted to analyze the zeros and some outer asymptotic properties of the so called Krall-type orthogonal polynomials. We study several examples, for perturbed measures supported in a finite or infinite interval on the real line. When the perturbed measures are semiclassical, an electrostatic interpretation of their zero distribution in terms of a logarithmic potential interaction of unit charges under an external field is given, and also, we extend the previous results by considering the sequences of polynomials orthogonal with respect to a m-iterated Uvarov perturbed Laguerre measure. These electrostatic interpretations have been reached by different techniques, from the coefficients of the holonomic differential equation that these polynomials satisfy. The second part of the memoir is focused on the so called Sobolev-type orthogonal polynomials of unbounded support. In particular we obtain some asymptotic properties and zero distribution for Laguerre Sobolev-type orthogonal polynomials. A relation between the pentadiagonal Jacobi matrix associated with the five term recurrence relation satisfied by the non-standard Sobolev-type orthonormal polynomials, and the tridiagonal Jacobi matrix associated with the three term recurrence relation satisfied by the standard two-iterated sequence of orthonormal polynomials is also given.
  09/2012, Degree: Doctor of Philosophy, Supervisor: Francisco Marcellán Español, Héctor E. Pijeira Cabrera