We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an appr...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

It has been recently discovered that exceptional families of SturmLiouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of exceptional orthogonal polynomials can be constructed by means of multiple-step algebraic Darboux transformations. The construction is illustrated with an examp...

In this paper, a numerical method, which is called the Laguerre collocation method, for the approximate solution of Lane–Emden type functional differential equations in terms of Laguerre polynomials are derived. The method is based on the matrix relations of Laguerre polynomials and their derivatives, and reduces the solution of the Lane–Emden type functional differential equation to the soluti...

We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

Stable and efficient spectral methods using Laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains. It is shown that spectral-Galerkin approximations based on Laguerre functions are stable and convergent with spectral accuracy in the usual (not weighted) Sobolev spaces. Efficient, accurate, and well-conditioned algorithms using Laguerre functions ...

Laguerre filters constitute an orthonormal basis for the Hilbert space, for this they are used in system identification and reduced-order modelling. In this paper a new property of Laguerre filters is introduced: it is shown that the system having as transfer function the sum of the first n + 1 functions has all the singular values equals each other. On the basis of this property a generalizati...

This paper presents a series of new results in modeling of the Grünwald-Letnikov discretetime fractional difference by means of discrete-time Laguerre filers. The introduced Laguerrebased difference LD and combined fractional/Laguerre-based difference CFLD are shown to perfectly approximate its fractional difference original, for fractional order α ∈ 0, 2 . This paper is culminated with the pre...

The scaled distribution of the smallest eigenvalue in the Laguerre orthogonal and symplectic ensembles is evaluated in terms of a Painlevé V transcendent. This same Painlevé V transcendent is known from the work of Tracy and Widom, where it has been shown to specify the scaled distribution of the smallest eigenvalue in the Laguerre unitary ensemble. The starting point for our calculation is the...