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On the Interpolation by Legendre Polynomials
On the Interpolation by Legendre Polynomialsopenaire +1 more source
Legendre-Gould Hopper-Based Sheffer Polynomials and Operational Methods
Symmetry, 2020 A remarkably large of number of polynomials have been presented and studied. Among several important polynomials, Legendre polynomials, Gould-Hopper polynomials, and Sheffer polynomials have been intensively investigated.
Talha Usman +2 more
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Families of Legendre–Sheffer Polynomials
Mathematical and Computer Modelling, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Subuhi Khan
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Recurrence Legendre Polynomials
Moscow University Mathematics Bulletin, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Note on Legendre Polynomials
International Journal of Nonlinear Sciences and Numerical Simulation, 2001Summary: 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 +2 more
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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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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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An inequality for Legendre polynomials
Journal of Mathematical Physics, 1994The 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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O(1) Computation of Legendre Polynomials and Gauss--Legendre Nodes and Weights for Parallel Computing [PDF]
SIAM Journal of Scientific Computing, 2012 A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1].
Jan Fostier, Bart Michiels
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A Novel Theory of Legendre Polynomials
Mathematical and Computer Modelling, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P E Ricci, G Dattoli
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Legendre Polynomials and Legendre Functions
2021Legendre 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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