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...

A simple structure of the multiple Laguerre polynomial expansions is used to study the Cesàro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an `1-radial function f0(|x|) is shown to be an `1-radial function that coincides with the Laguerre polynomial expansion of f0, which allows us to settle the problem of summa...

x : Mn-1 ? Rn be an umbilical free hypersurface with non-zero principal curvatures. Then is associated a Laguerre metric g, tensor L, form C, and second fundamental B, which are invariants of under transformation group. In this paper, we will study the parallel nonnegative or non-positive tensor.

has been prepared by th e National Bureau of Standards [1]; 1 th e introduction to the table gives a precise definition of this function. This table covers the range Ixl ~ 20, Iyl ~ 20, with argumcnts variously spaced. In order to compute E1( z) olltsid e this range, (or within this range, a t points where interpolation is awkward, which are those with comparatively large argument), several met...