Abstract
In this paper, we apply a sinc-Gaussian technique to compute approximate values of the eigenvalues of Sturm-Liouville problems which contain an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than that of the classical sinc method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.