Results 231 to 240 of about 516,382 (294)

Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications

Frontiers of Information Technology & Electronic Engineering, 2018
In this study, a new controller for chaos synchronization is proposed. It consists of a state feedback controller and a robust control term using Legendre polynomials to compensate for uncertainties. The truncation error is also considered.
S. Khorashadizadeh, M. Majidi
semanticscholar   +1 more source

Numerical solution of fractional pantograph equations via Müntz–Legendre polynomials

The Mathematical Scientist, 2023
M. Tavassoli Kajani
semanticscholar   +1 more source

An inequality for Legendre polynomials

Journal of Mathematical Physics, 1994
The following inequality is established: ‖Pn(cos ϑ)‖< [√1+(π4/16)(n+1/2)4 sin4 ϑ]−1, 0<ϑ<π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos ϑ) + (4/π2)× Q2n(cos ϑ) < [√1+(π4/16)(n+1/2)4 sin4 ϑ]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of ...
LAFORGIA, Andrea Ivo Antonio, Elbert, A.
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A Note on Legendre Polynomials

International Journal of Nonlinear Sciences and Numerical Simulation, 2001
Summary: We use an operational method to show that Legendre polynomials can be viewed as discrete convolutions of Laguerre polynomials. It is furthermore shown that they can be derived as the particular case of a new family of two-variable orthogonal polynomials, whose properties are studied with some detail.
Dattoli, Giuseppe, Ricci, Paolo E., Cesarano, Clemente   +2 more
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Associated Legendre Polynomial Approximations

Journal of Applied Physics, 1951
Approximations for the associated Legendre Polynomials are derived by a phase integral method. The method is an extension of the WBK method, applicable to separable multidimensional wave propagation problems.
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Wavelet collocation method based on Legendre polynomials and its application in solving the stochastic fractional integro-differential equations

Journal of Computer Science, 2021
A. Singh, M. Mehra
semanticscholar   +1 more source

Numerical solution of variable-order space-time fractional KdV–Burgers–Kuramoto equation by using discrete Legendre polynomials

Engineering computations, 2020
M. Heydari, Z. Avazzadeh, C. Cattani
semanticscholar   +1 more source

On Legendre's Polynomials

1976
Publisher Summary This chapter focuses on Legendre's polynomials. It discusses Kodaira's identity, Weyl's theory, Green's formula, symmetric boundary conditions, T-positive theory, S-positive theory, and other theorems.
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Expanding Legendre polynomials

Journal of Applied Analysis
Abstract The expansion of Legendre polynomials P ℓ ⁢
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The Radius of Starlikeness, Convexity and Uniform Convexity of the Legendre Polynomials of Odd Degree

Results in Mathematics, 2019
S. Bulut, O. Engel
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