(1-dimensional) Splines are functions defined over contiguous intervals delimited by knots. Between those knots, a spline is a low-degree polynomial function - but not the same function in every interval. Thus a spline can be characterized by its polynomial function coefficients in each segment.
Now, suppose instead of coefficients for a polynomial basis of functions, I choose some arbitrary functions. Again, their linear combination may differ between intervals.
What do I call such functions? That is, is there a commonly-used term for them? If not, would "generalized splines" do?