Evaluate the B-spline basis
Pyth - 83 82 bytes
Jesus, this is long, probably a few redundancies, but the formulas are long. This is a recursive solution that just implements the formulas given. The reference solution seems to be doing something else, but I don't know what. Maybe if I knew more about what all of this does...
KEM?H+.x*c-KJ@QG-@Q+GHJgGtHZ.x*c-=T@Qh+GHK-T@QhGghGtHZ&amp;|&gt;K@QGqK@QG&lt;K@QhGgRvzt-lQvz

Test Suite.