= Solution
In the normalized second-order <linear differential equation>, an <ordinary point> $z_0$ is one at which both $p$ and $q$ are <holomorphic functions> in a neighbourhood of $z_0$. A <singular point of a differential equation> is a point that is not ordinary. A singular point $z_0$ is a <regular singular point> if $(z-z_0)p(z)$ and $(z-z_0)^2q(z)$ extend analytically to $z_0$. Equivalently, $p$ has at most a simple pole and $q$ at most a double pole there. If a singular point fails this test, it is an <irregular singular point>. The normalized form matters: zeros of a leading coefficient must first be assessed after division by that coefficient.
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