1
University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China
(Leexu1244@yahoo.com)
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,
| Style | # |
|---|---|
| MLA | Lee Xu. "On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory." Galoitica: Journal of Mathematical Structures and Applications, Vol. 7, No. 2, 2023 ,PP. 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |
| APA | Lee Xu. (2023). On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 ( 2 ), 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |
| Chicago | Lee Xu. "On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory." Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 no. 2 (2023): 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |
| Harvard | Lee Xu. (2023). On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Journal of Galoitica: Journal of Mathematical Structures and Applications, 7 ( 2 ), 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |
| Vancouver | Lee Xu. On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 7 ( 2 ): 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |
| IEEE | Lee Xu, On Finding Legendre Polynomials by Algebraic Methods Based on Matrix Theory, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 7 , No. 2 , (2023) : 47-50 (Doi : https://doi.org/10.54216/GJMSA.070205) |