University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China
Email: 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.