Results 11 to 20 of about 516,382 (294)

Coordinating representation registers: linear algebra students' understanding of orthogonal Legendre polynomials in the inner product space ℙn in a technology-assisted learning environment [PDF]

open access: hybridAnnales de Didactique et de Sciences Cognitives, 2018
The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of the orthogonal Legendre polynomials as vectors of the inner product space ℙn in a DGS (Dynamic Geometry Software)-MATLAB ...
Günhan Caglayan
doaj   +2 more sources

On the Expansion of Legendre Polynomials in Bicomplex Space and Coupling with Fractional Operators

open access: goldAxioms
In this paper, we introduce a novel version of the Legendre polynomials in the bicomplex system. We investigate the essential properties of the Legendre polynomial, focusing on its bicomplex structure, generating functions, orthogonality, and recurrence ...
Ahmed Bakhet   +3 more
doaj   +2 more sources

Bi-Bazilevič functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials

open access: yesJournal of Mathematics and Computer Science, 2021
In this paper, using the Mittag-Leffler-type Borel distribution, the authors introduce a new class of bi-Bazilevic functions de-fined in the open unit disc associated with Legendre polynomials, we find estimates for the general Taylor-Maclaurin coefficients ...
S. El-Deeb   +2 more
semanticscholar   +1 more source

On the Elementary Symmetric Polynomials and the Zeros of Legendre Polynomials

open access: yesJournal of Mathematics, 2022
In this paper, we seek to present some new identities for the elementary symmetric polynomials and use these identities to construct new explicit formulas for the Legendre polynomials.
Maryam Salem Alatawi
doaj   +1 more source

Associated Conformable Fractional Legendre Polynomials

open access: yesJournal of Physics: Conference Series, 2021
Along with the work of Abul-Ez et al. [37], we introduce the associated conformable fractional Legendre polynomials (ACFLPs), from which the fractional differential equation of ACFLPs is established.
Haifa Shihab, Thair Younis Al-khayat
semanticscholar   +1 more source

On the estimation of functions belonging to Lipschitz class by block pulse functions and hybrid Legendre polynomials

open access: yesKarpatsʹkì Matematičnì Publìkacìï, 2020
In this paper, block pulse functions and hybrid Legendre polynomials are introduced. The estimators of a function $f$ having first and second derivative belonging to $Lip_\alpha[a,b]$ class, $0 < \alpha \leq 1$, and $a$, $b$ are finite real numbers, by ...
S. Lal, V.K. Sharma
doaj   +1 more source

Meshless local Petrov-Galerkin method for rotating Rayleigh beam using Chebyshev and Legendre polynomials [PDF]

open access: yesArchive of Mechanical Engineering, 2022
The numerical solutions are obtained for rotating beams; the inclusion of centrifugal force term makes it difficult to get the analytical solutions. In this paper, we solve the free vibration problem of rotating Rayleigh beam using Chebyshev and Legendre
Vijay Panchore
doaj   +1 more source

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