Legendre Polynomials: a Simple Methodology

Legendre polynomials are obtained through well-known linear algebra methods based on Sturm-Liouville theory. A matrix corresponding to the Legendre differential operator is found and its eigenvalues are obtained. The elements of the eigenvectors obtained correspond to the Legendre polynomials. This method contrast in simplicity with standard methods based on solving Legendre differential equation by power series, using the Legendre generating function, using the Rodriguez formula for Legendre polynomials, or by a contour integral.