\[hR^{\prime}_{n,t}=\frac{h^{n+1}}{(n+1)!}\left(f^{(n+1)}(\xi_{0})\frac{\mathrm{%
d}}{\mathrm{d}t}\prod_{k=n_{0}}^{n_{1}}(t-k)+f^{(n+2)}(\xi_{1})\prod_{k=n_{0}}%
^{n_{1}}(t-k)\right),\]