Singular integral equations with Cauchy type kernels are considered on a real interval. It is assumed that near the end points of the interval the solution of the Riemann-Hilbert problem diverges at most logarithmically. By using such an “end-point condition” in a simple case of neutron transport in a infinite medium, the evaluation of the continuum coefficients of the singular eigenfunction expansion is carried out easily. Moreover, it results that such coefficients have a structure completely analogous to that of the discrete coefficients, showing the intimate relationship between Case's continuum and dis crete modes.