Results 201 to 210 of about 4,323 (242)

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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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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Legendre Polynomials and Legendre Functions

2021
Legendre polynomials and, respectively, Legendre functions are one of the most important functions in physics. In this chapter, we will discuss and derive corresponding program codes supporting complex arguments and complex indices. The code is freely available.
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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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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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Gauss–Legendre polynomial basis for the shape control of polynomial curves

Applied Mathematics and Computation, 2023
Song-Hwa Kwon
exaly  

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

Mathematical Methods in the Applied Sciences, 2022
Zhi Li, Xiaoming Zhang, Jiangong Yu
exaly  

Thermoelastic guided wave in fractional order functionally graded plates: An analytical integration Legendre polynomial approach

Composite Structures, 2021
Xiaoming Zhang, Xianhui Wang
exaly  

Guided wave propagation in functionally graded fractional viscoelastic plates: A quadrature-free Legendre polynomial method

Mechanics of Advanced Materials and Structures, 2022
Zhi Li, Xiaoming Zhang, Lahoucine Elmaimouni   +2 more
exaly  

A Method for Forest Canopy Height Inversion Based on UAVSAR and Fourier–Legendre Polynomial—Performance in Different Forest Types

Drones, 2023
Hongbin Luo, Luo Hongbin, Cairong Yue
exaly