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arxiv: 1202.3971 · v1 · pith:FWCKVGKLnew · submitted 2012-02-17 · 🧮 math.SP

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

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keywords approximationasymptoticboundaryconditionseigenvaluesformgenerallambda
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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.

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