of $h_d$ is then given by $$h_d(t)
    = \sum_{n = 0}^\infty \left[
    \sum_{\ell = 0}^{d + 1} (-1)^\ell \binom{d + 1}{\ell} E_n(\ell + 1)
    \right] \frac{t^n}{n!}.$$ If $n \leq d$, from the first part of the proof, it follows immediately that $$D^n h_d(t) \big|_{t = 0}
    = D^n g_d(t) \big|_{t = 0} - D^n g_{d + 1}(t) \big|_{t = 0} = 0,$$ which proves (\[5.8\]).

Finally, we are ready to prove the conjecture (\[5.3\]).

The following holds for all cardinal B-spline degrees $d \geq 0$ $$\lambda_{\infty}^d = \frac{1}{d!} \cdot \begin{cases}
    T_d, & \hbox{$d$ odd,} \\
    E_d, & \hbox{$d$ even.}
  \end{cases}$$

To simplify the notation, let $L_d := d! \, \lambda_{\infty}^d$. Due to the symmetry of interpolation nodes, the sum in (\[5.2\]) can be written as $$\lambda_{\infty}^d = \sum_{j = -r}^r (-1)^j t_j^d, \quad
    t_j^d = N^d \left( j + \frac{d + 1}{2} \right), \quad j = -r, \ldots, r,$$ where $r = \lfloor d/2 \rfloor$. From (\[2.1\]) and (\[2.2\]), it follows that $$t_j^d = \frac{1}{d!} \sum_{\ell = 0}^{d + 1} (-1)^\ell \binom{d + 1}{\ell}
    \left( j + \frac{d + 1}{2} - \ell \right)_{+}^d.$$ Then $$L_d
    = \sum_{j = -r}^r (-1)^j
    \sum_{\ell = 0}^{d + 1} (-1)^\ell \binom{d + 1}{\ell}
    \left( 