## Abstract

It is a standard result that the eigenvalues associated with the equation $\nabla ^{2}\psi $ + {$\lambda $ - q(r)} $\psi $ = 0, where q(r) is a function of r only, and tends to infinity as r $\rightarrow \infty $, are the roots of equations of the form $\int_{R_{1}}^{R_{2}}\left\{\lambda -q(r)-\frac{(l+\frac{1}{2})^{2}}{r^{2}}\right\}^{\frac{1}{2}}$ dr = (m + $\frac{1}{2}$) $\pi $ + $\epsilon _{m}$, where l and m are integers, and $\epsilon _{m}$ is small when m is large. It has recently been proved that they are also the roots of equations of the form $\int_{0}^{p}$ {$\lambda $ - q(r)}$^{\frac{1}{2}}$ dr = ($\frac{1}{2}$l+m + $\frac{3}{4}$) $\pi $ + $\eta _{m}$, where $\eta _{m}$ is also small when m is large. By a direct comparison of the integrals involved, this paper shows the two expressions to be consistent.

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