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.