The Legendre-Stirling numbers are the coeffi cients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejoh...

A novel and eective method based on Haar wavelets and Block Pulse Functions(BPFs) is proposed to solve nonlinear Fredholm integro-dierential equations of fractional order.The operational matrix of Haar wavelets via BPFs is derived and together with Haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. Our new met...

An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

Scalar multiplication on Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic cur...

We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data co...

The mollification obtained by truncating the expansion in wavelets is studied, where the wavelets are so chosen that noise is reduced and the Gibbs phenomenon does not occur. The estimations of the error of approximation of the mollification are given for the case when the fractional derivative of a function is calculated. Noting that the estimations are applicable even when the orthogonality o...

Abstract— This paper introduces a new set of orthogonal moments function hypergeometric based on the discrete Legendre polynomials. The Legendre moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain o...

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ball...

Student, Assistant Professor Associate Professor Lendi Institute of Engineering and Technology, VZM, INDIA. Abstract: The peak side lobe level (PSL) is numerically estimated for Rudin-shapiro sequences and Legendre sequences which belong to the families of Binary sequences. Notable similarities are presented between PSL and merit factor behavior under cyclic rotations of the sequences (i.e. 1/4...