The computation of eigenvalues of singular Sturm-Liouville operators

The problem of computing eigenvalues of a singular Sturm-Liouville problem is reduced to the computation of eigenvalues of a Hilbert-Schmidt infinite matrix. The uniform convergence of the generalized determinant allows for the approximation of eigenvalues by the finite section. A key feature of the method that leads to a fast algorithm is to combine generating functions with the Laplace transform to compute explicitly the entries of the matrix without numerical integration. Published by Elsevier Inc.