Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 7E / a

The point $z_0$ is an ordinary point when both $p$ and $q$ are holomorphic at $z_0$.

The point $z_0$ is a regular singular point when it is singular butextend holomorphically to $z_0$.

A singular point which is not regular singular is an irregular singular point: at least one of $(z-z_0)p(z)$ and $(z-z_0{)}^{2}q(z)$ fails to extend holomorphically to $z_0$.