$N$-dimensional Bessel and Jacobi processes describe interacting particle systems with $N$ particles are related to $\beta$-Hermite, $\beta$-Laguerre, $\beta$-Jacobi ensembles. For fixed there exist associated weak limit theorems (WLTs) in the freezing regime $\beta\to\infty$ $\beta$-Hermite $\beta$-Laguerre case by Dumitriu Edelman (2005) explicit formulas for covariance matrices $\Sigma_N$ te...

We introduce two new non-iterative approaches towards passivity enforcement for scalar rational transfer functions. The first is based on the projection of the Herglotz-Cauer representation of the transfer function on the orthonormal Laguerre basis. The second is based on the rational approximation by means of Talbot-Gauss quadrature of a pertinent integral related to the Cauer transform kernel.

Let f(z) = e−bz 2 f1(z) where b ≥ 0 and f1(z) is a real entire function of genus 0 or 1. We give a necessary and sufficient condition in terms of a sequence of inequalities for all of the zeros of f(z) to be real. These inequalities are an extension of the classical Laguerre inequalities.

Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in closed-form and to produce an expression for this average value as a finite sum.

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and ...

This paper is concerned with the estimation of the nominal yield curve by means of two complementary approaches. One approach models the yield curve directly while the other focuses on a model of the forward rate from which a description of the yield curve may be developed by integration of the forward rate specification. This latter approach may be broadly interpreted as a generalisation of th...

We obtain several formulas for the action of the bilinear Hilbert transform on pairs of Hermite and Laguerre functions. The result can be expressed as a linear combination of products of Hermite or Laguerre functions.

Discrete-time Laguerre series are a well-known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model.

Discrete-time Laguerre sequences are eeective for representing sequences in the form of orthogonal expansions. The main objective of this communication is to propose a systolic-array implementaion for nite-duration Laguerre expansions.

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