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 ...

In this paper, the conformable Laguerre and associated differential equations are solved using Laplace transform. The solution is found to be in exact agreement with that obtained power series. addition some of properties polynomial discussed Rodriguez's Formula generating function proposed proved

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 ...

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...

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...

Laguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form 〈p,q〉S = ∫∞ 0 p(x)q(x)x αe−x dx + λ∫∞ 0 p′(x)q′(x)dμ(x), where α > −1, λ 0, and p,q ∈ P, the linear space of polynomials with real coefficients. If dμ(x) = xαe−x dx, the corresponding sequence of monic orthogonal polynomials {Q n (x)} has been studied by Marcellán et al. (J. Comput. Appl. Math. 71 (1996) 24...

In this paper we address the problem of approximating functions on a semi-in nite interval by truncated series of orthonormal generalized Laguerre functions. The generalized Laguerre functions contain two parameters, namely a scale factor and an order of generalization. The rate of convergence of a generalized Laguerre series depends on the choice of these parameters. Results concerning the det...

Following the program for finite translation planes to construct such planes from collineation groups in the translation complement a search for nonMiquelian Laguerre planes of odd order is initiated. In this note finite Laguerre planes of order p2 , P a prime, are investigated. If such a Laguerre plane .c admits a circle-transitive elation group and an automorphism group of order p2 in the ela...