Normalized Marsden dual functional (${\lambda }_i(p)={\sum }_{j=0}^{k-1}(-1{)}^j{p}^{(j)}(x){\psi }_i^{(k-1-j)}(x)$)

When the knot polynomial is normalized as ${\psi }_i(x)={\prod }_{\ell =1}^{k-1}(x-t_{i+\ell })/(k-1)!$, the displayed formula has no additional factorial prefactor. Applied to Marsden's identity, it extracts the coefficient of the corresponding B-spline in any polynomial of degree at most $k-1$. Differentiating the finite sum makes adjacent terms cancel, proving independence of $x$. For linear polynomials the coefficient is their value at the Greville abscissa.