Results 11 to 20 of about 155,769 (214)
On polar Legendre polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2010 We introduce a new class of polynomials $\{P_{n}\}$, that we call polar Legendre polynomials, they appear as solutions of an inverse Gauss problem of equilibrium position of a field of forces with $n+1$ unit masses. We study algebraic, differential and asymptotic properties of this class of polynomials, that are simultaneously orthogonal with respect ...
Cabrera, H. Pijeira +2 more
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An Orthogonality Property of the Legendre Polynomials [PDF]
Constructive Approximation, 2016 We give a remarkable additional orthogonality property of the classical Legendre polynomials on the real interval $[-1,1]$: polynomials up to degree $n$ from this family are mutually orthogonal under the arcsine measure weighted by the degree-$n$ normalized Christoffel function.
BOS, LEONARD PETER +3 more
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Orthoexponential polynomials and the Legendre polynomials [PDF]
Applications of Mathematics, 1978 summary:Orthoexponential polynomials can be expressed in terms of the Legendre polynomials. The formulae proved in this paper are useful for the computation of the values of orthoexponential polynomials.
Jaroch, Otakar
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On the interval Legendre polynomials
Journal of Computational and Applied Mathematics, 2003 This paper deals with the extension of the classical Legendre polynomials to the interval theory by considering the family of interval polynomials \(\mathbb L_{n,k}(x) \) satisfying, for each natural number \(k\), the recursive formula \(\mathbb L_{0,k}(x)=[1-\frac 1k,1+\frac 1k]\), \(\mathbb L_{1,k}(x)=[1-\frac 1k,1+\frac 1k]x\), \(\mathbb L_{n+1,k}(x)
Patrı́cio, F. +2 more
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Integrals of Legendre polynomials and approximations
CoRRWe derive some identities and relations and extremal problems and minimization and Fourier development involving of integral Legendre polynomials.
Rehouma, Abdelhamid
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Investigating the Properties and Dynamic Applications of Δh Legendre–Appell Polynomials
MathematicsThis research aims to introduce and examine a new type of polynomial called the Δh Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δh Legendre–Appell polynomials and explore their properties.
Noor Alam +3 more
doaj +2 more sources
, 2016 Legendreovi polinomi rješenja su Legendreove diferencijalne jednadžbe \left(1-x^{2}\right)P^{n}-2xP^{'}\left(x\right)+\lambda P\left(x\right)=0. Pomoću ove diferencijalne jednadžbe također se može dobiti funkcija izvodnica.
Marjanović, Katarina
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Properties of Clifford-Legendre Polynomials [PDF]
Advances in Applied Clifford Algebras, 2022 Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra ${\mathbb R}_m$.
Ghaffari, Hamed Baghal +2 more
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Euler and the Legendre Polynomials [PDF]
, 2023 In this note we will present how Euler\u27s investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the Legendre ...
Aycock, Alexander, Alexander Aycock
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A Property of Legendre Polynomials [PDF]
Proceedings of the National Academy of Sciences, 1970 Remark I: The Legendre polynomials are the spherical functions for the symmetric space SO(3)/SO(2). A property analogous to that stated in the above theorem holds for other symmetric spaces. In this fashion we get also new properties for Gegenbauer polynomials, Bessel, and Legendre functions.
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