Generalizations of an integral for Legendre polynomials by Persson and Strang

Legendre polynomials for numerical solution of linear fuzzy Fredholm integral equations

Legendre polynomials Triple Product Integral and lower-degree approximation of polynomials using Chebyshev polynomials

In this report, we present two mathematical results which can be useful in a variety of settings. First, we present an analysis of Legendre polynomials triple product integral. Such integrals arise whenever two functions are multiplied, with both the operands and the result represented in the Legendre polynomial basis. We derive a recurrence relation to calculate these integrals analytically. W...

development and implementation of an optimized control strategy for induction machine in an electric vehicle

in the area of automotive engineering there is a tendency to more electrification of power train. in this work control of an induction machine for the application of electric vehicle is investigated. through the changing operating point of the machine, adapting the rotor magnetization current seems to be useful to increase the machines efficiency. in the literature there are many approaches wh...

Generalizations and Specializations of Generating Functions for Jacobi, Gegenbauer, Chebyshev and Legendre Polynomials with Definite Integrals

In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials. Specializations of generating functions are accomplished throu...

An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations

In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations usi...