Monomial B-spline coefficients
= Monomial B-spline coefficients
{title2=$a_i^{(m)}=e_m/\binom{k-1}{m}$}
For order $k$ <B-splines>, comparison of coefficients in the <Marsden identity> gives
$$
t^m=\sum_i\frac{e_m(t_{i+1},\ldots,t_{i+k-1})}{\binom{k-1}{m}}N_i(t),\qquad0\leq m\leq k-1,
$$
on the basic knot interval. Here $e_m$ is the <elementary symmetric polynomial>, with $e_0=1$. The $m=0$ case is partition of unity; the $m=1$ coefficients are the <Greville abscissae>.