= Sturm-Liouville formulation with Bessel order as eigenvalue
{c}
{title2=$(xy')'+\beta^2xy=n^2y/x$}
For fixed $\beta$, move the order term of the <Bessel equation> to the right: $x^2y''+xy'+\beta^2x^2y=n^2y$. The <integrating factor> for its leading differential expression is $1/x$, giving the displayed <Sturm-Liouville theory> form with coefficient $p=x$, potential $q=\beta^2x$, weight $w=1/x$ and <eigenvalue> $n^2$. The origin is a singular endpoint. The <integrating factor> must be normalized from a positive reference point; its defining logarithmic <integral> cannot literally start at zero. <Boundary conditions> are needed before this differential identity becomes a specified self-adjoint spectral problem.
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