On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory

Lee

doi:https://doi.org/10.54216/GJMSA.070205

Full Length Article

Volume 7 • Issue 2 • PP: 47-50 • 2023

On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory

Lee Xu ^1*

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¹University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.070205

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Received: March 27, 2023 Revised: June 28, 2023 Accepted: August 26, 2023

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Abstract

This paper is dedicated to find Legendre polynomials by using novel linear algebraic methods based on matrices based on Liouville-Sturm theorem, where we find the matrix of the differential operator for Legendre polynomials, with their eigenvalues and their eigenvectors. Also, we illustrate many examples to clarify the validity of our work.

Keywords

Legendre polynomials differential operator eigenvalue eigenvector.

References

[1] L. C. Andrews, Special functions of mathematics for engineers, SPIE, USA, (1998)

[2] A. P.Raposo et al., Romanovski polynomials in selected physics problems, Central European journal of physics, 5(3), (2007), 253-284.

[3] V. Aboites, Laguerre polynomials and linear algebra, Memorias sociedad Matematica Mexicana 52 (2017), 3-13.

[4] V. Aboites, Hermite polynomials through linear algebra, International Journal of Pure and Applied Mathematics 114 (2017) , 401-406.

[5] V. Aboites , Easy Route to t-chebycheff polynomials, Rev . Mex. Fis., (2018)

[6] M. Ramirez, Simple Approach to Gegenbauer polynomials, International Journal of Pure and Applied Mathematics , (2018) Ref . AP2017-31-5266,

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Xu, Lee. "On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 7, no. Issue 2, 2023, pp. 47-50. DOI: https://doi.org/10.54216/GJMSA.070205

Xu, L. (2023). On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Galoitica: Journal of Mathematical Structures and Applications, Volume 7(Issue 2), 47-50. DOI: https://doi.org/10.54216/GJMSA.070205

Xu, Lee. "On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory." Galoitica: Journal of Mathematical Structures and Applications Volume 7, no. Issue 2 (2023): 47-50. DOI: https://doi.org/10.54216/GJMSA.070205

Xu, L. (2023) 'On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory', Galoitica: Journal of Mathematical Structures and Applications, Volume 7(Issue 2), pp. 47-50. DOI: https://doi.org/10.54216/GJMSA.070205

Xu L. On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Galoitica: Journal of Mathematical Structures and Applications. 2023;Volume 7(Issue 2):47-50. DOI: https://doi.org/10.54216/GJMSA.070205

L. Xu, "On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 7, no. Issue 2, pp. 47-50, 2023. DOI: https://doi.org/10.54216/GJMSA.070205

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