I am trying to prove the following property of a B-Spline. Given a natural number, m, the B-Spline N_m has the following property:
int_from negativ infinity to infinity(N_m(x)dx) = 1
I know that I am supposed to make a proof by induction, I am just not sure how to do it exactly. I have shown that the property is true for m = 1. So now I am supposed to show that the property holds for m+1, right? But how do I do it?
Thanks in advance