A Matrix-Eigenvalue Method to Compute Sturm-Liouville Polynomials

Abstract

Summary: Recently the Legendre and other Sturm-Liouville (SL) polynomials were found as eigenvectors of certain matrices. However, the proposed algorithms are computationally incomplete and do not lead to general formulas to calculate the coefficients of SL polynomials of any order. In this paper, we complete the algorithms based on a matrix-eigenvector method, which can be used to compute SL polynomials of any order. This includes Legendre, Hermite, Laguerre, and Chebyshev polynomials.