Laguerre Functional Model has many advantages such as good approximation capability for the variances of system time-delay, order and other structural parameters, low computational complexity, and the facility of online parameter identification, etc., so this model is suitable for complex industrial process control. A series of successful applications have been gained in linear and non-linear p...

Analogs of Laguerre and Meixner orthogonal polynomials in the algebra of symmetric functions are studied. The work is motivated by a connection with a model of infinite-dimensional Markov dynamics.

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...

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...