  In this paper, we derive an asymptotic approximation to the eigenvalues of
the linear differential equation $$ -y"(x)+q(x)y(x)=\lambda y(x), x\in (a,b) $$
with boundary conditions of general form, when $q$ is a measurable function
which has a singularity in $(a,b)$ and which is integrable on subsets of
$(a,b)$ which exclude the singularity.
