A note on a paper of Harris concerning the asymptotic approximation to the eigenvalues of $-y"+qy=\lambda y$, with boundary conditions of general form

Abstract

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.