Definition:Spline Function/Order

Definition
Let $\closedint a b$ be a closed real interval.

Let $T := \set {a = t_0, t_1, t_2, \ldots, t_{n - 1}, t_n = b}$ form a subdivision of $\closedint a b$.

Let $S: \closedint a b \to \R$ be a spline function on $\closedint a b$ on $T$.

Some sources, instead of referring to the degree of a spline, use the order.

Let the maximum degree of the polynomials $P_k$ fitted between $t_k$ and $t_{k + 1}$ be $n$.

The order of $S$ is then $n + 1$.