What is B-spline coefficient?

Question

I am programming with spline interpolation method in my work, and I am using an interpolate module from Scipy, specifically to use cubic spline interpolation. On the documentation (https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.splrep.html) it says that interpolate.splrep returns vector of knots, the B-spline coefficients, and the degree of the spline, but I do not know exactly what they are. I read various numerical analysis books on it and still did not find any precise definitions of them. I would appreciate anyone's help greatly.

Answer 1

A spline function has the form:$$f(x)=\sum_{i=0}^nc_iB_i(x)$$ where $c_i$ are the coefficients. $B_i$ are basis functions, each of which is determined by $d+2$ successive knots, where $d$ is the degree. This wikipage shows the recursive formula for $B_i(x)$ given $d+2$ knots.