The complexity measures of the Crámer-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calvet) types of the Rakhmanov probability density ρn(x) = ω(x)p 2 n(x) of the polynomials pn(x) orthogonal with respect to the weight function ω(x), x ∈ (a, b), are used to quantify various two-fold facets of the spreading of the Hermite, Laguerre and Jacobi systems all over their corresponding orthogona...

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials introduced by Cariñena et al., [3]. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical...

in this paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

Recently an upsurge in research relating to Laguerre filters for use in system optimization [1], system identification [2] and reduced-order modeling [3] has been noticed. The main reason for the good performance of Laguerre filters is that they form a uniformly bounded orthonormal basis in Hardy space [1]. Another reason, and this represents the novelty of the work carried out in this paper, i...

The purpose of this paper is to construct a unified generating function involving the families higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using their functional equations, we investigate some properties these Moreover, derive several connected formulas relations including Miller–Lee polynomials, Laguerre Lagrange Hermite–Miller–Lee

Solutions of the homogeneous 2D scalar wave equation of a type reminiscent of the “splash pulse” waveform are investigated in some detail. In particular, it is shown that the “higher-order” solutions relative to a given “fundamental” one, from which they are obtained through a definite “generation scheme”, come to involve the relativistic Hermite polynomials. This parallels the results of a pre...

This paper presents a numerical method for the approximate solution of mthorder linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this article is to present an efficient numerical procedure for solving mth-order linear delay difference equations with variable coefficients. Our method depends mainly on a Laguerre ...

Abstract. For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to L∞ norm, which generalize analogous results obtained for little qLegendre, little q-Jacobi and little q-Laguerre polynomials, b...

The second author dedicates this paper to the one and only Dick Askey, his mathematical father. Abstract. Three specializations of a set of orthogonal polynomials with " 8 different q's " are given. The polynomials are identified as q-analogues of Laguerre polynomi-als, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.