Hello,

Assuming that a B-spline $\displaystyle N_{m}$ is defined for some $\displaystyle m \in \mathbb{N}$ then the B-spline $\displaystyle N_{m+1}$ is defined by:

$\displaystyle N_{m+1}(x)=\int_{0}^{1}N_{m}(x-t))dt$

How can I, through induction, show that:

$\displaystyle \int_{-\infty}^{\infty}N_{m}(x)dx=1$

Suggestions would be greatly appreciated.