Computing the Fourier transform and its inverse is important in many applications of mathematics, such as frequency analysis, signal modulation, and filtering. Two methods will be derived for numerically computing the inverse Fourier transforms, and they will be compared to the standard inverse discrete Fourier transform (IDFT) method. The first computes the inverse Fourier transform through di...

A new tool for real-time characterization of both systemic and local circulatory hemodynamics has been developed. Given two peripheral circulatory waveform measurements this new signalprocessing algorithm generates two low order models that represent the distinct branch dynamic behavior associated with the measured circulatory signals. The framework for this methodology is based on a multi-chan...

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...

In 2009, Gómez-Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a secondorder differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are theX1-Laguerre and theX1-Jacobi po...

For α = n− 1, n ∈ N\{0}, the operator D2 is the radial part of the sub-Laplacian on the Heisenberg groupHn (see [2, 4]). These operators have gained considerable interest in various fields of mathematics (see [1, 4]). They give rise to generalizations of many two-variable analytic structures like the Laguerre-Fourier transform L, the Laguerre-convolution product, the dispersion and the Gaussian...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

In 2009, Gómez–Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a second– order differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are the X1-Laguerre and the X1-Jacob...

We construct flat Laguerre planes that admit the universal covering group of SL2R, extended by a factor R, as a group of automorphisms. These planes contain the affine Moulton planes as derived planes, and they are constructed by gluing together two copies of a Moulton plane, folded up along their fixed lines. The action of the Moulton group carries over (modulo Z2) to the Laguerre planes, and ...

An efficient method for evaluating inner products of repeated integrals and derivatives of a function described by a Laguerre model is presented. An immediate and promising application is model reduction of infinite-dimensional transfer functions. r 2004 Elsevier B.V. All rights reserved.

A novel power series representation of the generalized Marcum Q-function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a convergence speed analysis by means of truncation error. A brief review of related studies and some numerical results are also provided.