Results 11 to 20 of about 136,517 (223)
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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Generalized Legendre Polynomials
Journal of Mathematical Analysis and Applications, 1993 Let \((\lambda_ n)_{n\in\mathbb{N}}\) be a sequence of distinct real numbers with \(\lambda_ n>-1/2\). The authors orthogonalize the functions \(\{x^{\lambda_ 1},x^{\lambda_ 2},\dots\}\) with respect to the inner product \(\langle f,g\rangle:=\int_ 0^ 1 f(x)g(x)dx\) by using Gram-Schmidt-orthogonalization.
Mccarthy, P.C. +2 more
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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On the interval Legendre polynomials [PDF]
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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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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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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About the Legendre type operators [PDF]
E3S Web of Conferences, 2021 The article considers Legendre type operators acting in the corresponding weight separable Hilbert spaces. The choice of these spaces is due to the fact that these operators preserve all properties of the Legendre operator acting on L2 (-1,1).
Maleko Evgeny
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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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مجلة العلوم البحتة والتطبيقية, 2020 The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
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