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My book on differential equations says that $x_{0}$ is a regular singular point of the differential equation $P(x)y'' + Q(x)y' + R(x)y = 0$ if $(x - x_{0})\frac{Q}{P}$ and $(x - x_{0})^{2}\frac{R}{P}$ have convergent Taylor series about $x_{0}$. This criteria seems tedious to check because it means I have to expand $\frac{Q}{P}$ and $\frac{R}{P}$ as Taylor series, etc. Is there an easier way to check if a point is regular singular?

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Seen this? The idea is to check for poles... –  J. M. Nov 5 '11 at 14:24

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