Results 161 to 170 of about 53,695 (215)

An effective hybrid method for the optimal control of fraud rumor propagation on online social networks. [PDF]

Sci Rep
Khanduzi R, Jajarmi A, Ebrahimzadeh A.
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Full-cycle prediction of crack healing in self-healing concrete using generalized polynomial chaos expansion. [PDF]

Commun Eng
Fu C, Xu W, Zhan Q, Chen C, Guo T, Zhang X, Pang B.   +6 more
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Buckling behaviour of rectangular and skew plates with elastically restrained edges under non-uniform mechanical edge loading. [PDF]

PLoS One
Wang C, Liu Q.
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Legendre polynomials and irrationality

ALLADI, K., Robinson, M.L.
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Recurrence Legendre Polynomials

Moscow University Mathematics Bulletin, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Reverse Legendre polynomials

Archiv der Mathematik, 2022
Let \(\mathcal{P}\) be the vector space of all polynomials, equipped with the inner product \(\langle f(x), g(x)\rangle=\int_{-1}^{1} f(x) g(x) d x\). The Legendre polynomials \(P_{0}(x), P_{1}(x), \ldots\) are the polynomials obtained by applying the Gram-Schmidt procedure to the ordered basis \(\mathcal{B}=\left\{1, x, x^{2}, \ldots\right\}\) of ...
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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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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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