Let $f(z) := \sum_{n \geq 1} a_n z^n$ with $a_n \in {\Bbb C}$ be a power series ring such that the radius of convergence is equal to $1$.
Suppose that for the chosen point $\alpha$ such that $|\alpha| = 1$, i.e. a point on the unit circle $C$, the limit $\underset{z \to \alpha}{\mathrm{lim}} \, f(z)$ always coincides with the fixed finite value, which we denote by $f(\alpha)$, under any path inside $C$.