Regular singular point at infinity
= Regular singular point at infinity
Under $\zeta=1/z$, the point $z=\infty$ is regular singular for
$$
y''+P(z)y'+Q(z)y=0
$$
exactly when $zP(z)$ and $z^2Q(z)$ are <holomorphic function>[holomorphic] functions of $1/z$ near $1/z=0$.