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Galoitica: Journal of Mathematical Structures and Applications

Volume 7 , Issue 2 , PP: 47-50, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory

Lee Xu 1 *

  • 1 University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China - (Leexu1244@yahoo.com)

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

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

    Cite This Article As :
    Xu, Lee. On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 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, (), 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 , no. (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 , () , 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. (): 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, vol. , no. , pp. 47-50, 2023. DOI: https://doi.org/10.54216/GJMSA.070205

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