ordinary point

A point where both coefficient functions of a linear ODE are analytic, so a plain power-series solution works.

A point $x_0$ is an ordinary point of $y''+p(x)y'+q(x)y=0$ if $p$ and $q$ are both analytic at $x_0$ -- guaranteeing a power-series solution $y=\sum_{n=0}^{\infty}a_n(x-x_0)^n$ exists, with radius of convergence at least as large as the nearest singularity's distance from $x_0$ .